Counting House is best when you have your deck in the discard. Naturally, the obvious way to accomplish this goal is with Chancellor. The problem this faces is the sheer improbability of drawing your Chancellor, plus your Counting House, plus a +Actions card, amidst all your Copper. It’s OK, but pretty difficult to pull off.
The better (and cooler) way is with Golems. Build a deck of many Golems and a single Counting House, with no other Actions. Each time you play your Golem, it will find your Counting House, then discard your entire deck searching for another action (unsuccessfully). At that point, play your Counting House and draw all the Copper in the deck into your hand. Rinse and repeat.
This approach suffers from its flaws as well—it’s inflexible, for starters. Counting House has many synergies (Bank, Coppersmith, Warehouse), but none of them would work well with this strategy, which explicitly depends on the existence of only one non-Golem Action card in order to discard everything else. Moreover, it requires quite a few Golems in order to be effective, and ironically enough, suffers greatly when you actually draw your Counting House as part of your hand. (Though you can always hope your opponent will play Minion or Militia.) But the biggest advantage this combo has over Chancellor/Counting House is the ability to buy further Coppers without gumming up your combination. If you have enough Golems to reliably draw at least one each turn, then as long as you buy a single Copper along the way, you can guarantee a $8 turn every turn.