Instead of traditional CCG play in which gameplay starts after you've constructed your deck, gameplay in Dominion evolves WHILE building your deck. You start off with the same ten cards in your deck (a few coins and victory point cards) and your goal is to build a deck that will allow you to have the most victory points in it when one of the end-game conditions is reached.
When laid out, the "board" will look something like this (an image of the Brettspielwelt implementation of the game):
![Image](http://images.boardgamegeek.com/images/pic385302_md.jpg)
You start out with a five-card hand drawn from your starting deck of ten cards and use those cards to perform actions, buy, and then "cleanup". Effectively what ends up happening is that cards you buy go into a discard pile which, when your playdeck runs out, are shuffled together to form your new playdeck. As an example, this means that any cards you buy in the first turn of the game are going to be back in your hand and ready for use on turn 3 (since each turn you play an action, buy a card, then discard your entire hand before drawing five new cards).
The real meat of the game, though, comes from the starting configuration. In the screen image above, the Kingdom card set the game is being played under is in the middle, the ten Kingdom cards including Moat, Cellar, et al. This is the "base set", or the set of cards that the developer recommends playing with on your first play. The interaction of these cards provides an IMMENSE amount of depth. For example, one strategy you could pursue is going coin-heavy, using Remodels to upgrade your high-value coins (gold) to provinces, the highest-VP building you can purchase. This tends to be a "fast" deck. Another possibility: using combinations of villages (2+ actions, +1 additional card) and markets (+1 action, +1 card, +1 buy, and +1 coin), balanced out by coin cards, to string together ridiculous combinations of cards. All the while you need to balance the amount of "treasure" (which is your "income" in this game) and the victory point cards (which are useless for anything except end-game scoring) in your hand to keep your deck humming along.
There are 24 different kingdom cards. That means the number of different possible starting configurations are nearly infinite, especially when you choose your configuration randomly. The rules, however, offer some other suggestions for configurations based on the type of game you'd like to play. WAnt a game where money abounds? Try the "Big Money" setup, using Adventurer, Bureaucrat, Chancellor, Chapel, Feast, Laboratory, Market, Mine, Moneylender, and Throne Room. Due to the "race" nature of the game it can seem like it's not very interactive at times... want a more interactive approach? Try the "Interaction" setup - Bureaucrat, Chancellor, Council Room, Festival, Library, Militia, Moat, Spy, Thief, and Village.
If anyone's interested in checking this out on Brettspielwelt I'd be glad to show you how to play.