Hearthpwn

Cards: Shielded Minibot, Acolyte of Pain, Aldor Peacekeeper, Consecration, Ironbeak Owl, Zombie Chow
With coin: Wild Pyromancer, Truesilver Champion, Consecration

If you already have a fairly strong opener with strong cards like Minibot or Muster, keeping an equality along with a Muster / Pyromancer is okay. However, you do NOT want to keep equality and consecration in your opener as it's way too slow.

Just try to stabilize early game with your strong value cards, and close to midgame you should've gotten board control. Healing up and developing a board is key and you should have the game by now. You'll eventually draw into too many heals and taunts and they won't be able to get through.

I don't think the cards really need an explanation as to why they're kept, they're just generally really good to stabilize. Use minibots to trade and Owl for example an enemy Mad Scientist or a Knife Juggler.

P.S: Keep an equality in your backpocket if you've already established boardcontrol, as aggro can sometimes attain boardcontrol later into the game - and the boardclear will help reestablish yours.

 Cards: Aldor Peacekeeper, Truesilver Champion, Piloted Shredder, (Sludge Belcher if your hand is great), Acolyte + Peacekeeper and Shielded Minibot, Pyromancer + Equality, Harrison Jones (if against a weapon class and you already have decent early game in your hand), Zombie Chow
With coin: Very similar, however you can almost always keep Sludge Belcher.

Generally you just want to outvalue your opponent early game, and by keeping an Equality boardclear combo you can easily stabilize. Sometimes your opponent gets too fast of a start and you'll need to simply survive until you can clear the board and gain boardcontrol, and simply heal back up afterwards.

Once you've gained boardcontrol against midrange they won't be taking it back easily, using Sylvanas and Tirion you'll shut them down lategame.

Don't be afraid to aggressively use Aldor Peacekeeper as the constant damage from minions can easily stack up. If it even gets rid of 2-3 or maybe even 1 damage depending on the circumstances that's good enough. Equality and Big Game Hunter will deal with their eventually bigger targets.

 Cards: Aldor Peacekeeper, Equality combos (yes, consecration or pyromancer are both fine), Acolyte of Pain, Shielded Minibot, Truesilver Champion, Piloted Shredder, Sludge Belcher, Harrison Jones (if against weapon class), Emperor Thaurissan (if your other opening cards are okay)
With coin: Pretty much the same as without, although Thaurissan is more often a great keep and Pyromancer + Equality becomes stronger.

In this matchup you want to take it very easy, efficiently deal with their minions and try to use your heropower as much as possible after the early turns (so around turn 1-5). Whenever you're about to use an equality combo, ask yourself (do I really have to use this?) and if it's actually going to work out. It's important to also keep in mind that sometimes you'll have equality with pyro and consecrate, and then you need to think about which of the two you want to use in combination with Pyromancer. Sometimes keeping the pyro is better, but often you'll be using the pyro and save the consecrate for later turns.

Drag the game out and play your cards as efficiently as possible, the main cards in this MU is Nefarian, Tirion Fordring and Sylvanas Windrunner. Use them wisely, however, don't for example sit around on Tirion forever just to dodge any whatsoever possible removal. That's not how you want to play this deck, and avoiding the 8-cost play for a less efficient turn than perhaps turn 8 may cost you the game. Even if he dies he spawns the Ashbringer which will carry you into the lategame.

Try to draw cards when you can, so if you have an opening for it use your Lay on Hands (even if it doesn't always heal, as the ridiculous amount of healing in this deck will negate that loss later), or simply an Acolyte of Pain. However, you want to most often try and protect your Acolyte behind a taunt so it doesn't die to a weapon. If you're up against a spellheavy class like Mage then there's not much you can do about it to guarantee the draw, so instead just play it when it fits you and where it would seem as killing it efficiently would ruin their curve.

Grim Patron Warrior:

Simply play as you would against a midrange, but save your equality combos for their big patron turn (8-9 and onwards). Watchout so that you're not about to get OTK'd by some weird Frothing Berserker, so keep taunts and your health up if you can. Once they've used their two patrons and you've cleared the board this matchup is incredibly easy, as you can simply deal with their worse cards and heal out of range for anything weird.

Face/Hybrid Hunter:

Mulligan: Owl, Minibot, Muster, Pyro (with coin preferably), Consecration and Truesilver (both preferably with the coin).
It's fairly similar the two of them, you want to desperately mulligan for early game. If you have coin then keep Pyromancer and eventual spells, Holy Light is a great way to deal 1 damage across the board potentially clearing 1 health creatures whilst getting you back in the game. If you desperately need to deal 2 dmg across the board, on turn 3 playing Pyromancer + Coin + Holy Light on yourself is a great way to come back into the game, with a potential truesilver follow up.

Once you've established a decent board then you can easily deal with their threats and heal out of range, but keep in mind that you want to play safe - so healing will often go BEFORE board control plays (dependent on the situation at hand).

Warlock

This is one of the easiest matchups. Simply keep Peacekeepers and equality combos, along with strong early game minions and you'll quickly get board control. If you somehow lose it simply clear it with equality. Against demonlock this matchup is similarly played as to handlock, you get rid of their initial threats (being Drake/Giant/Piloted Shredder/Imp Gang Boss) and then slowly grind them out. Against handlock keep a combo to deal with potential molten giants, or simply a BGH and 8 dmg on the board. 

Keeping an owl against voidcallers is great, although keep in mind it can be bad to keep early game. Generally however it is an MVP against any Warlock due to drakes/voidcaller. Also, keep in mind what'll happen if you kill a voidcaller, so have a Peacekeeper/BGH ready for it just incase.

Lastly, against Zoolock: This is this decks probably worst matchup. Mulligan aggressively for early game cards as in Minibot, Muster, Acolyte, Pyro and Owl, and just do your best to survive. If you manage to clear the board you have a great chance to comeback, however ALWAYS keep in mind how easily a Zoolock can refill their board - never consider the game won until their health is either 0 or they have no cards in hand!

Teacher/Oil Rogue

Play it like you would against other midrange decks, use Harrison preferably on an Oiled/Poisoned dagger, and try to avoid playing Tirion as the sap will often lose you the game.

Control Warrior

Very easy matchup, play like you would against control. Keep an equality for their potentially big minions, and save Owl for Sylvanas (!). Don't overextend into brawl and expect a long game, Nefarian and Sylvanas / Equality boardclears will be key.

Druid:

Play against them as you would with any midrange deck. Keeping Peacekeepers are great for innervated minions, and try to keep an equality boardclear in your backpocket as the board will often spin out of control. Play your Acolyte on turn 3 as it will often interrupt their curve, or bait out a keeper which would be a lot worse on Tirion/Sylvanas/Belcher.

Of course, always try to stay out of combo range (14 damage) and account for any addition of damage from minions on their board (minions attack + 2 attack from savage roar).

I have not yet written about Priest/Shaman/Paladin/(?) as I believe they're not very prominent on ladder. Simply look at the general matchup guide to get help against those, but if you feel some are being more played than others please comment and I'll add the matchup write up as soon as I can.

So here are all cards explained as to why they're in the deck, and also potential card replacements for certain hot topics.

Zombie Chow: This was added instead of a Muster for Battle, simply to counter the more aggressive meta and to avoid certain combos (Patron Warrior, Unleash). Overall a great 1-drop that helps this deck curve out nicely. Possible replacement: Abusive Sergeant. In combination with Silverhand Recruits, BGH (giving an enemy minion +2 attack), and just any other minion to trade upwards - it can be a great card in this deck. Also playing it on turn 1 against aggro is also fine.

Equality: Mainly used for boardclears, it helps you dealing with big enemy minions. In combination with Wild Pyromancer + Potential Spell or Consecration it will often be used to it's greatest extent. A keycard in the deck, use it wisely!

Holy Light: Can be used to heal yourself for 6, to heal a minion, or to simply in combination with Pyromancer deal 1 damage across the board. Keep in mind, if you can, use this combination: Equality + Wild Pyromancer + Random Spell, instead of Wild Pyromancer + Equality, as this will let you have a 3/1 pyromancer still on the board. This can of course not be done unless you have an extra spell that you're able to use in the same turn. Potential replacements are Seal of Light, however I still value the potential of healing for 6 on a minion a lot, which is why I'm still running Holy Light>Seal of Light

Ironbeak Owl: Running one silence, indicating that it should be used wisely. On for example Sylvanas Windrunner or other important minions, it can also be used on Mad Scientists/Acolytes of Pain depending on matchup. In aggro matchups the card can be used much more freely than otherwise, as you simply want to survive. Silencing a Knife Juggler is often a good idea.

Shielded Minibot: Simply one of the best two drops in the game, often trading 2-for-1 and helping you establish board control. Can be used along equality to trade upwards for free!

Wild Pyromancer: In combination with random spells, Equality or Consecration is what makes this card shine. Keep in mind, Pyro + Spell with an Acolyte on the board is a great way to potentially guarantee two carddraw!

Acolyte of Pain: To give the deck that extra little bit of carddraw to get your boardclears, Acolyte is an obvious pick. At very least it will replace itself, but often in combination of Pyro + Spell, or Aldor Peacekeeper will give more than one card. Potential replacements for this would be Solemn Vigil, which I am still experimenting with!

Aldor Peacekeeper: Great card that perfectly deals with your opponents threats, just an overall amazing card that is put in almost all Paladin control decks. 

Big Game Hunter: Deals with 7+ attack minions, being often Dr. Boom, Giants, Ragnaros, Alexstrazsa and so forth. Just a great card, but only running one as there aren't that many targets, and if there are - the boardclears will deal with them.

Truesilver Champion: One of the best paladin cards in the game, giving you a huge amount of tempo - whilst healing your for 4. Cannot be replaced (nor should it have to..)

Consecration: Once again, a great paladin card to help with trading or clear boards filled with weak minions. In combination with Wild Pyromancer or Equality it definitely has a spot in this deck and could be considered a core-card. 

Piloted Shredder: Great 4 drop, often trading 2-for-1, or helping you trade upwards against your opponent. Potential replacement is Kezan Mystic as they have very similar stats, but it's entirely meta-based. So if you're up against Hunters and Mages, consider taking out one and putting in Kezan!

Antique Healbot: 3/3 for 5, with a whopping heal for 8! This will almost always be used to heal for the entire value, or close to it, and so I deem it to be an important card. Against aggro this will often be a lifesaver, and even against control you will often need the healing (as they will of course try to kill you at one point), and it can also get you out of combo range against certain decks (for example Druid's FoN + Savage Roar). Could be replaced by another 5 drop, or Quartermaster - however I find this card to be too valuable to take out.

Harrison Jones: Wonderful card, giving you carddraw, cardadvantage, and a decent 5/4 body on the board! Drawing your boardclears is key, and this guy gives you everything you want. Removing a weapon, gaining tempo, and a card is absolutely perfect. This card is entirely meta-based, so if weapon classes are running dry on ladder, simply switch him out forLoatheb!

Sludge Belcher: Great 5-drop, against aggro and control/midrange. Can stop potential lethal combos and will help you either trade immediately, or trade upwards using the 3 attack, or the slime. Just a really good card as it is split into two, and it can be used in combination with Equality to still have the 1/2 slime, which will trade with potential more 1-health creatures after the equality. Replacements: None, just get naxx :) If you absolutely can't, try other 5-drops although they will not work nearly as good.

Emperor Thaurissan: Core-card of this deck! Will let you use your combos for much less mana, giving your more space to play around with in terms of mana. Will also allow you to heal more in one turn which could be game deciding against some decks (Freeze mage, Aggro, Druid). Replacements would be other good 6-drops, mainly looking at The Black Knight.

Sylvanas Windrunner: Core-card, giving you an enormous threat on the board - and also allowing you to regain board control. A #1 priority in this deck! Replacements: None really do enough, but Mind Control Tech or other good 6-drops can work.

Guardian of Kings: Oh man, this is what this deck was centered around originally. Great value, also giving a nice amount of heal. A potential change is to take out one GoK for Dr. Boom, which I definitely think is a viable replacement. However, they're a very big part in the deck and I recommend making core-changes with caution. 

Lay on Hands: One of the absolute keycards in the deck, and cannot be replaced. Craft this before even considering making this deck, or any other control paladin! It cannot be replaced by any card, but the carddraw could be achieved through another Acolyte of Pain, but the healing + carddraw is what makes it good. Craft it!! SwiftRage

Tirion Fordring: Also one of the main reasons as to why this deck is viable, often going for a nice 5-for-1 in value it's a key component in this deck. Cannot be completely replaced, but another big card for example Kel-Thuzad, Ysera or Ragnaros could be a thing - HOWEVER, they do not entirely do what is required for this deck to be viable! Do not expect anywhere near similar results if you're not playing Tirion, he is that good.

Nefarian: Main reason as to why this deck was created, and works! Giving you two potentially extremely valuable cards (as they are always classcards) it is a staple in this deck and shouldn't be removed. Potential replacements are Ysera, however I do not value the dream cards anywhere near the same amount as classcards, since Ysera is too random. Ysera Awakens is of course a great card, but I prefer Nefarian still - as he also gives you cards in the same turn. So in combination with Thaurissan you might be able to play those spells in the same turn, which can be game deciding and it has been many times for me.

So yeah, those are my card explanations!