The basic idea behind this deck is to always put your opponent in a position to trade unfavorably. Most minions in the deck trade 2-for-1 or require at least some additional removal to be taken care of which mostly results in your opponents turn being non mana-efficient.
This deck does not run the typical Force of Nature + Savage Roar combo. By removing these 2-4 cards from the deck, you give yourself lots of play room for situational cards that are more efficient than clearing a board with your combo pieces that are meant to end the game (in a Druid mirror match against this deck, the opponent more often than not will be forced to FoC your board in order to clear, ruining his win condition).
Basics, Mulligans, and Matchups:
In almost all matchups, fish for your low-cost cards: Zombie Chow, Faerie Dragon, etc. A good hand against aggro includes those mentioned above, with wrath/innervate/keeper of the grove. Faerie Dragon in the early game lets you establish a good position on the board because of its inability to be effected by target spells. Innervating a Keeper of the Grove on turn 2 is a very powerful play against aggro because of its immediate impact on the board and it's 4-health body which will take a couple hits against small creatures.
Double Tazdingo means he will more often than not, come to your rescue against aggro. Use your big body cards wisely. Cub, Grove Tender, Keeper, and Sen'jin will keep you ahead of the game and allow you to outlast your opponent until you need to pop Alexstrasza.
If you've reached the point in the game where you've effectively used Alex either aggressively or defensively, the game is probably yours (and no, it is not hard to survive until turn 9 with this deck).
Against other control decks (basically just Druid and Warrior), play it slow. You don't want to run out of cards too quickly. A warrior matchup will run to fatigue, so using Alex wisely is extremely important there. Playing conservatively against Druids will result in them having to use their combo pieces to wipe your board which = GG. Combo Druids will run their hands dry before you to keep up on the board while you are sitting comfortably with 4+ cards in your hand waiting for them to play something worthwhile.
An earlier version of this deck ran Geddon in place of Dr. Boom, but it wasn't helping as much as Starfall so I replaced him with Dr. Balanced himself. You could also consider swapping Black Knight or Ancient of Lore for Ragnaros.
If you like the deck, give it a +1. I'm a huge control lover and will probably post more decks similar to this one for other classes. Please post feedback as it benefits everyone who reads, and remember to have fun! ( ͡° ͜ʖ ͡°)