1) Remember at all times that no matter how tired you are, your partner is almost certainly much more tired. Basically, give her a free pass for the first few months, if not longer. (The hormonal changes a few days in are no fun either)
2) There is no point just comforting a crying baby - they just don't understand what you're trying to do. Distract the fuck out of them instead. (This from a baby psychologist on a BBC documentary. Obviously if something is actually wrong then fix it.)
3) Babies are their own tutorial. They start off really simple, with about three things to remember, and then once you've got the hang of those things they start adding new ones on. But you don't need to panic about whether you can do it, it's not complicated, just full on.(This was excellent advice Adam gave me before Sophia was born)
4) Bonding - do not panic if it takes you six months (or longer) to fall in love with your child. I certainly felt incredibly protective of Sophia from the moment she was born, but I didn't feel fully connected to her until she was able to smile at me, and we could have some kind of interaction. It's really easy to feel awful because all the TV and movies says it happens instantly, but it can take a fair while, so don't worry about it. (Thanks to Hal for this one)
5) Ignore any advice you don't like.
 or Spring Forth from. Or Request An Exit Visa from. I've lost track of the current terminology.
Original post on Dreamwidth - there are comments there.