If you like Yogg, then why not play him as many times as possible in one game?
With this deck, you can potentially have his effect for an infinite number of times (limited by the turn timer of course).
Compared to decks like Yogg Mage, Yogg Druid, and Yogg Hunter where Yogg is only played once or a maybe few times with some copy effects, Yogg Shaman is the best Yogg deck because you can simply get his effect many more times per game. Even compared to Yogg Rogue where you can shuffle 40 Yoggs into your deck with Togwaggle's Scheme, this deck is better because it can consistently get more than 40 Yogg effects and is much more resilient to the problem of Yogg overdrawing you into fatigue.
Infinite Yogg-Sarron Package (necessary to get Yogg's effect for an infinite number of times)
Yogg-Saron, Hope's End - the master of RNG.
Shudderwock - replays battlecries and is used to go infinite and replay Yogg's battlecry many times per game.
The way this deck goes infinite with Yogg-Saron, Hope's End effects is by playing infinite Shudderwocks and having Shudderwock play Yogg's battlecry. For the first time you play Shudderwock, make sure you have played Grumble, Worldshaker and a Saronite Chain Gang at a minimum beforehand, and that you have the hero power from Corrupt the Waters. On the Shudderwock turn or before, play Tour Guide to get a free hero power, and then use the hero power and Shudderwock in one turn. Alternatively, you can use Lightning Bloom instead of Tour Guide to be able to hero power and play Shudderwock in the same turn. This will guarantee your Shudderwock going infinite, but you can play Shudderwock without the hero power and still have a chance. You can play Yogg-Saron, Hope's End either before or after your Shudderwock turn, and afterwards keep using your zero cost hero power (each Shudderwock will make it cost zero again) and play your Shudderwocks which will keep generating new ones and replaying Yogg's battlecry. It's usually better to play Shudderwock before Yogg-Saron, Hope's End to get multiple copies of Shudderwock in hand because Yogg's battlecry can destroy a Shudderwock before it gets to duplicate itself and add copies to your hand. Try to keep your hand size low when you play him so that there is room for copies to go into your hand. One final note is that if you are against a deck with low pressure and have drawn Yogg, you can play Shudderwock for many turns to keep filling up your deck with cards from the Anti-Fatigue package battlecries. Then when your deck is at the limit, 60 cards, you can play Yogg and then the Shudderwock chain and it will keep going for quite a while.
Anti-Fatigue Package (prevents fatigue damage during your infinite Yogg turns)
Body Wrapper - shuffles a card into your deck and helps prevent fatigue
Baleful Banker - shuffles a card into your deck and helps prevent fatigue
This package is incredibly important to this deck. When you are playing Shudderwocks to get the Yogg effect each time, Yogg can draw cards from your deck. Over time, this will kill you due to fatigue damage unless you can shuffle more cards into your deck. As many copies of Body Wrapper and Baleful Banker should be played as possible given the amount of pressure you are facing from your opponent before going into your infinite Yogg turns, so that each time you play Shudderwock for the Yogg effect it also uses those battlecries to shuffle cards into your deck and thus help prevent fatigue. These cards also help complete your quest. Try to play Baleful Banker with no friendly minions on the board because you don't want extra cards in your deck while you are still trying to draw your combo pieces of the Infinite Yogg-Sarron package. Also, be aware that shuffling a card into your deck will randomize the deck order so don't play these after Lorekeeper Polkelt until you have drawn the cards you need.
Card Draw and Spells Package (Cards to draw through your deck quickly and get to your combo including useful spells drawn by Spirit of the Frog)
Spirit of the Frog - draws cards, the spells below synergize with this to draw a spell of higher cost.
Maelstrom Portal - helps you survive to your combo turn.
Tidal Surge - good removal and heal.
Lorekeeper Polkelt - doesn't actually draw any cards but he will put your key combo pieces on top of your deck.
Spirit of the Frog is a great card that lets you draw through your deck very quickly. In addition, you can predict the next card you are going to draw from it. An important point is that you should not try to maximize the number of spells you cast with Unstable Evolution, because if the spell count is too high then Yogg will draw more cards on average than the Anti-Fatigue package can shuffle in to your deck, which might cause you to die from fatigue. Around 10 spells from both Unstable Evolutions is a good limit. Primal Dungeoneer is another great card to draw spells and Grumble, Worldshaker.
Mulligan for Spirit of the Frog, Questing Explorer, Primal Dungeoneer, and Armor Vendor. Draw cards to get to your Infinite Yogg-Sarron package and play those cards while naturally completing your quest through playing battlecry cards including the Anti-Fatigue package. Finally, play the combo described in the Infinite Yogg-Sarron package and keep playing Shudderwocks each turn that will each replay Yogg's effect twice due to the quest hero power. Sit back and enjoy!
This is an incredibly fun deck to see the power of Yogg-Saron, Hope's End. You can swing for lethal early on if he makes you a board or keep the Yogg effect going for as long as you want and have Shudderwocks to play (although this deck can go infinite, if Yogg decides to discard your hand and transform your deck, then there is not much you can do -- however one of the Anti-Fatigue package cards might shuffle a Shudderwock into your deck so if your hand is discarded a Shudderwock may be in your deck). Other than playing this deck in casual or ranked, it might be fun to play a friend match with it, letting your opponent borrow this deck, and then agree to not do any direct face damage and let Yogg decide the outcome of the match.
I hope you enjoy this deck and that this guide is helpful! If you have any questions, suggestions, or stories about this deck, please comment below.