Dominion is an elegant 2-4 person card game that takes 20-45 minutes. There are Action cards which modify the flow of the game, Treasure cards needed to buy any of the three types of cards, and finally Victory cards, the aim being maximizing victory points.
The turn order does not change throughout the game. During their turn, players take (A)ctions as allowed by cards, (B)uy new cards, (C)lean-up the unused cards in their hands, and (D)raw five new cards.
Some randomness is necessary in each game. But it should be such that the players should feel capable of reducing it. Here it comes about because of the cards you draw at each turn. You need to have a right mix of cards to consistently draw useful ones. And which cards you have is determined by which cards you buy, and when you buy them. If there are too many (or even few) victory points, they are of no use. Even if you have many treasure cards, you can buy only one item. Action cards are the real modifiers. If there are too many stand-alone (or terminal) actions, you can use only one of them. Some action cards like village and market allow you to take additional actions as well as draw more cards. The market and militia provides you additional virtual money etc. One can buy multiple copies of the same card. Ten different action cards are available and deciding a strategy around a few of them is useful. There is generally not much point in trying to buy one or a few of each.
Most cards do not interact with other players ('Attack'), and so the game goes on independently in some sense. The players are not even (generally) competing for resources. But then there are cards like militia which affect the number of cards that other players hold. Or an action like thief can steal money from others. A single card, moat, repeals the attacks but then one may need to have several copies of it.
Pacing of the game is important and that is what you need to be able to control despite the random draw of five cards from your deck. If you could get most of your cards in your hand everytime, then you are guaranteed to win. So that should be one possible aim. It is the choice of the right action cards to buy at the right time that can make or break your game. Another thing to remember is that initially victory cards are a hindrance, but you need them to win. So, as the game progresses, you need to start collecting them. Especially the higher valued ones. This is also linked to the game end condition. The game ends when the stack of the highest valued victory points is over or any three stacks are over. This end condition of finishing 3 stacks can be hastened and one has to watch out for that. Thus there are interesting parallels from Puerto Rico (Money/Actions first, then Victory points or ending the game by building on the 12 available building spots) as well as Power Grid (Hold back initially so that you can go full speed later).
But there is more once you get accustomed to the standard set of 10 action cards (also called ‘kingdoms’). You can choose any set of 10 action cards out of a possible 25 sets, thus making available a large number of variations. There is a set, for instance, which ensures that there can be a lot of money in circulation. Or another involving several different attacks.
It takes some time for one to realize one slightly odd point of the game: all cards in your "hand" get discarded at each turn (clean-up). Now that I have told that up front, you should be able to get into the game better. The cards get shuffled into your hand when all cards have been used.
Once the mechanism is understood a game can get over in about 20 minutes making it a quick game (especially for the 2-person version). Some cards are clearly more versatile than others, but the remaining 9 action cards do ensure that a single card can not be a runaway winner. The action modifiers have to be judiciously used, and victory points need to be accumulated at the correct times. Because of the balancing, just as you start getting into the groove, the game is almost over.
Bottomline: I like it because of the variations possible, the need to hold back and the feeling that one is in control.