Most important thing- attitude. Act like you've been there before. Be cool. The operator and the DP need to trust you so when they ask you if you can do something, as long as you know it's physically possible, nod, look thoughtful, and say "sure" like you were asked if the sky's blue. If you know it can be done, you'll figure out a way to do it.
Don't ask the operator how the shot was after each take. If it sucked, believe me, they'll tell you. All you're doing is annoying the operator and showing your insecurity.
Have fun. Make the people around you laugh when you get the chance. If you don't have a sense of humor, wear a funny hat. (ok, if you don't have a sense of humor you don't realize that's a joke). Making movies should be fun.
Be the operator's extra eyes on set. You're a camera operator too. Look for reflections, look for cables, look for shadows. It ain't all about the moves. They'll appreciate you for this because, trust me, a lot of guys don't do this.
Mark the front wheels. The chassis kicks around on dance floor and back wheel marks can't be trusted.
Know your eyelines. Know the rule, know where they are throughout a scene. You'll be amazed how much this helps you be a better dolly grip. Plus, there's nothing better than informing the DP/operator that the eyeline he's just set up is wrong.... and being correct. It freaks them out.
Learn what you can and can't get away with. This comes mostly with experience, but you'll learn when you can get away with little shortcuts such as not having to level the track completely, when the floor will work fine, and other things that will save you time.
Make friends with the electricians. They can be your best friend, or worst enemy. For some reeason, juicers love the dolly. I can't tell you how many times I've been away from the dolly doing something else and a juicer stepped in and covered me for a second by booming up and inch or sliding left or right. You also need the electricity they provide or it'll be a long show.
Protect the lens. Look for flares. Flag 'em (unless they want them).
Marks aren't everything. It ain't about getting from one to two, it's about what the camera sees. If you think it's all about the marks then you don't have a chance. (This doesn't mean it isn't important to hit your marks, but there are times when it's more important to have the camera in the right place than hit a mark. You only learn these times, ironically, by not watching your marks.)
Endeavor not to suck.
That's all for now. There are some very good veteran Dolly Grips who read this site (and one who posts on it from time to time). I welcome them to add their own tips in the comment section and I'll add them to this post.