Well, it depends on my position. If I'm Player 2, and there's an attack with Player 1 advantage (Sea Hag, Militia, Cutpurse, etc.) I'll veto that. If I'm Player 1, I try to pick what my strategy will be, and then veto the thing that will get in the way of my strategy. Barring that, I'll usually veto the typical high variance cards (Familiar, Treasure Map) or sometimes alternative Victory card strategies - e.g., Duke which I'm not 100% confident with as a strategy.
I'll let "trap" cards stand if there's a good out for me (Pirate Ship if there are +$ actions on the board, Alchemist if there's no +buy and it's a Province game, Possession if there are good attacks), in the hopes that my opponent will go for the trap.
I know some are opposed to the veto mode, but I don't mind it.. it's like a game within a game... I don't care enough to click "require" on the Automatch, but I do think it's sort of fun.