Whoa! Dont compound anything! First if you are not interested in a detail shop removing them for you start like this. Wash your car, then before drying it clay bar the whole thing. Rinse it down and dry it. You can then use a cleaner wax or a hard shell wax with a LIGHT coating. Wipe that all off. Check for swirls. If they are still there, go get the 3M swirl remover, it is a light polish that will get out a lot of the swirl marks. Swirl marks are caused by numerous things, Machine car washes, Wheeling out your car to much, bad waxing techniques, etc... What color is your car again?
Dude, you just said "Dont compound anything" then told him to clay bar it then use a rubbing compound (3M swirl is a rubbing compound).
Clay bar should be done every once in a while, but is not neccesary in this case as claying your car pulls up sap, tar, road grime, etc, but the bar won't solve your swirl problem.
There are a couple different way of dealing with swirls, and it really depends how deep into the detailing rabbit hole you wanna go. I say dive all the way in, gotta learn somehow, right? Polish it with a light rubbing compound (I like
these), seal it with a paint sealer (I swear by
this stuff, but any good sealant will do), then hit it with your favorite wax, but make sure you don't get a wax that has cleaners or sealant built into the formula, you just need a top coat. Everyone seems to like poorboys paste wax, but it's a pain to put on without a Random Orbital polisher. My money goes to
Zaino, but I've heard amazing things about Ultima products, and I'm trying
this one next week. It's pricey, but according to everyone I've heard from, the ease of application and quality of protection more than make up for it.
If you dont want to do anything so drastic, get a one stage polish/cleaner/wax like
Klasse AIO and go to town, but I can't guarantee results with the easier approach.
Now to address the problem of making the swirls. Swirl marks are not circular in any way, they are straight lines in your paint caused by rough surfaces touching your paint. Being inexperienced in this field, I'm willing to bet you have a wash mit from the local autozone, maybe use a towel to dry the car? These two things will cause more swirls than just about anything else you do to the car. If you use a cheap wash sponge or mit, or a car wash that is not sudsy enough, particles of dirt get trapped in the mit and cause dozens of long, thin scratches (swirl marks). A towel that is not 100% pure cotton will further scratch the paint while you dry. You should always air dry with an electric leafblower or use microfiber towels to avoid dragging particulate around your paint.