To fix this, you need a buffer, wool pad and compound. This all can be had fairly cheap at Harbor Freight.
You will see at the store, there will be different "cuts" from fine to heavy. The fine cuts use a foam pad and heavy cuts use a wool pad. Look closely on the meguiars bottles...the correct pad to use pretty much pictured right on the front of them. I would go for the wool pad and a medium/light cut to start. This will probably get you good results without buying everything. Just be light and don't dig into one spot on the paint too hard.
I've worked at a detail/body shop for a few years and this is pretty much what all the people in the industry use. The fiber towel/rubbing compound stuff you see at auto part or retail stores isn't bad but you can get great results with a real buffer.