You should check the radiator resevoir every so often. Make sure there is water/antifreeze in there. If there is in there, there should be some in the radiator. If there's none in there, you need to take the radiator cap off (when the car is cool) and check to make sure there's fluid in there.
You should keep your tires rotated every like 5000 miles I'd say. Just look at the front ones to see if they are wearing around the edges.. more so than the back then you'd need to get them switched. Also check your tire pressure. You can get a cheap tire pressure guage for like $2 at an auto supply store. It should say on your tire what the max air pressure should be. Keeping your tires at the right pressure will save you from buying new tires too soon, and/or possibly save you from a tire blowout.
I check my oil every couple weeks to make sure I'm not losing any. I will add a quart myself in between oil changes because my car seeps oil.
I would take your car to one of those drive through oil change places when its time. They check for a lot of other stuff while they're changing your oil which is cool... they've saved me some money by catching problems before they get to an advanced stage.
Cars are a big pain in the ass.