If your neighbor keeps disturbing you, you can sue, and ask the court for money damages or to order the neighbor to stop the noise ("abate the nuisance," in legal terms). For money damages alone, you can use small claims court. For a court order telling somebody to stop doing something, you'll probably have to sue in regular court.
Of course, what you really want is for the nuisance to stop. But getting a small claims court to order your neighbor to pay you money can be amazingly effective. And suing in small claims court is easy, inexpensive, and doesn't require a lawyer.
To win, you'll need to show:
To prove your case, use police reports, witnesses, your own testimony, or even a recording.
How much money should you sue for? In most states, small claims courts limit judgments to between $2,500 and $7,500. (For the amount in your state, see How Much Can I Sue for in Small Claims Court?) Requesting $20 a day for your trouble would probably be considered reasonable. If the noise problem is really severe -- keeping you from sleeping or working and making you completely frazzled -- make it $100 a day.
You can learn more about small claims court in the Small Claims Court area of Nolo's website.