It's a simple bit of advice, given to me by a seasoned dad many years ago. Advice which I always try and pass on to stressed out new dads whose babies won't sleep.
The advice is this: Try and stay relaxed. Even if it is 3.30am and you've been up for the tenth time that night. If you are relaxed you'll probably get back to sleep a little quicker. If you're awake most of the night but have managed to stay relaxed there's also more of a chance you'll cope with the day ahead a little better.
Of course, if staying relaxed is more than you can manage, console yourself with the knowledge that my children have, between all three of them, managed to keep me and my wife awake most nights, for most of the night, for the last seven years. We're still here to tell the tale but damn, I'm tired!