How does Intrigue change your general Dominion strategy?
Intrigue generally has nastier attack cards than Base does, and you really need to avoid getting hit by them or at least learn how to deal with their fallout.  The three major attacks are:

Saboteur:


This is the only card in the game that can force you to trash a Colony or Province (and not get one back).

Swindler:


This allows your opponent to force you to trash a card and give you one of the same cost.  Essentially, they can dilute your deck, and even give you Curses if you trashed a Copper.

Luckily, for Colony and Province, this just wears down their respective piles, as the cost has to be the same.  Note: For any card, if there is no card of the same cost left, you just lose that card.

Very late Edit: There is one other card that costs 8... Peddler.  I suggest not playing a game with both Peddler and Swindler in play.

Torturer:


A nasty card, particularly when used with Base's Throne Room or Prosperity's King's Court.  Unlike Militia, Ghost Ship, or Goons, Torturer does not stop when you only have three cards.  Also of note is that the Curse goes into your hand should you choose to take it, so you can use it with things like Chapel when your turn rolls around... or if it's King's Courted, take two curses then discard them for the third.

There is one more attack card (Minion) and two pseudo-attack cards (Masquerade and Tribute; they're not attack cards, so you can't block them)... you really should look through all the Intrigue cards to see what they do.