It looks like you've gotten some great advice, but I thought I'd add my two cents. We get something that works for awhile, and then our daughter (18 mos) decides she doesn't want to do it again so we have to come up with another gimmick. She has almost all of her teeth, so I really worry about making sure they get cleaned. For every stage, we've always brushed our teeth at the same time so she sees it's something we do, too. Here are the things we've done:
First, I would sing "Brush-a, brush-a, brush-a" like in "Grease" and she thought that was funny and distracted her enough I could get a quick once over before she shut her mouth tightly.
The next step was letting her brush my teeth while I brushed hers. That worked for the longest phase.
Then after that stopped working, we got some baby toothpaste (hadn't been using anything before) and started taking turns. She got her turn first and she'd suck on it for awhile while I brushed my teeth, and then I'd get to have my turn.
Now she doesn't always let me have my turn, so I play "upside down baby" which is a distraction we use a lot. For teeth brushing, I sit down and tilt her back (she automatically opens her mouth when she's slightly upside down), and get a decent brushing in.
There are still times when I don't get a chance to do it, and I don't make a big deal out of it, even though it bugs me, because I don't want it to become a constant struggle. We usually brush in the morning and and night so if one of those times doesn't pan out, I either try another time during the day, or just let it go.
Good luck!