Changing oil is easy, it's the other experiences that are tough. :P
All you do is lift the car up, unscrew the oil plug bolt and let it drain into a bucket, unscrew the oil filter and let that drain, screw in the new filter, screw the oil plug back in and then fill the engine with the correct oil. (Mobil 1 5W-30 synthetic - the original formula in the silver bottle is fine) and you want a Mobil-1 M-113 Oil Filter. All of this and more can be found at Autozone. Never hurts getting to know your car a little more either.
In the meantime, yeah, I'd definitely call around for some reputable businesses in the private sector. Just remember, just because a place has bad reviews doesn't mean it is bad. Most people who have good experiences with a business never bother leaving a review because they don't see any reason to.
Let us know how it goes, and make sure to check out South Florida's local Camaro clubs (there's a thread at the top of the Florida region page) if you really want to take your interest in your Camaro to the next level.