Obviously what Goons really wants is a Village engine of some kind: you get the most value out of your Goons by playing more than one at a time, since the number of VP pellets you can get per turn increases quadratically per the number of Goons played on that turn. But what if there are no Villages, and so you can't play multiple Goons per turn? Well, at least you want to get the maximum points out of each Goons you
do play, right? But this involves using up all your buys, which usually involves filling your deck with undesirable cheap cards.
This is where Apothecary comes in. Apothecary fits into a Goons deck very neatly in several ways:
1 - Early in the game, when your deck is mostly Coppers, Apothecary will put a lot of Coppers in your hand each turn, bringing you closer to that all-important first Goons.
2 - Once you're using your Goons, you can use up your extra buys on Coppers with more or less impunity: if you have enough Apothecaries in your deck, you'll filter the extra Coppers out as you go and they'll only rarely seriously clog your progress. Moreover, keeping a lot of Coppers in your deck means that each Apothecary you play is likely to add to your buying power for the turn even into the late-game.
3 - An engine built on cheap Alchemy cards often wants a source of +buy, so you can buy those Apothecaries in say a $5P hand and still be able to get a Silver or Cellar or something else useful with the rest of your money; Goons provides that +buy.
<a href="
http://dominion.isotropic.org/gamelog/201112/08/game-20111208-173455-e509bd35.html">Here's</a> a log of a Goons/Apothecary game I just played; I used both buys on every Goons turn I had, ending up with five Apothecaries and eleven Coppers (and would have had more if not for my Moneylender), whereas my opponent only averaged one and a half points per Goons play. Cellar was a key support card here in a way it isn't often in handsize-attack games; Cellar interacts with Apothecary beautifully, since Apothecary both increases handsize and gives you a look at what's coming up in your deck so you know whether or not you want to Cellar out some of those Coppers.
Related strategies: Goons / Counting House; Goons / Philosopher's Stone. Also Goons/Gardens, although if you're going heavily for Gardens it can be hard to make it to $6 frequently to get Goons.