The second installment in the dominion series, Intrigue series adds multi-type cards (like "Action - Victory") and more complex actions and attacks. It also includes the common cards from the base set like Copper and Provinces, so that it can be purchased and played as a stand-alone game. Its theme is choice; several cards require players to choose between options. Intrigue provides 25 new kingdom cards.
The Dominion rules are extraordinarily comprehensive. For questions regarding how cards interact, if you can, check the individual card entries in the appropriate rulebook(s) and you'll probably find your answer there. A PDF of the Dominion: Intrigue rules is available here.