It helps if you bring lots of things for the kid to do, and if you bring movies check and see if they have a dvd/video player. Make sure everything is G-rated, PG depending on the movie/kid.
Check with the parents about their rules for the kid and what happens when other kids come over. They might have rules about games they can and can not play, etc.
Also, when playing a game, while it is important for kids to learn how to lose gracefully. Don't win too much. I learned this one the hard way.
I might be sort of a pushover babysitter, so I have trouble with this one, but be firm in what you say. Don't believe the, "but mommy lets me do this" unless mom has told you it's OK.
If you end up with dirty dishes, do the dishes as much as possible. You may not be able to load them in the dishwasher or anything but make sure to at least rinse off if not clean them with soap and water. I got chewed out by a parent for this one when I raised my rates. I raised them to $10 from $5, but offered her $9, but this was because I was a good deal older than when I first started babysitting for them and I was getting this amount from other families and it was becoming the norm rate for babysitting. And her kids were nightmares. When she got home she started going crazy because I hadn't washed the dishes, and because I raised my rates she expected me to do more in terms of cleaning and everything. She gave me this huge lecture, and then told me to go wash the dishes. I did, just because I wanted to get our of there, and there weren't just the dishes from my visit, but it seemed like the past two days. I rinse them, load them, and she starts going crazy because shes running late. Their house was a mess too, it was completely unsanitary.
Anyways, just make sure your rates are clear, get the numbers from the parents, stuff like that. Just remember that you are not obligated to continue babysitting for anybody. If you're not comfortable in a house then just refuse to babysit the next time around. Also, since you're taking a class, youll be quite a hot commodity.
Good luck!