While this 'ible will detail the repair process for the front brakes, the procedure for the rear brake caliper is the same. The steps also show the removal and re-installation of the brake pads, so you can use this guide for changing your brake pads as well. Think of this as a twofer!
Before you do anything, please be aware that proper functioning brakes are critical to your safety as well as the safety of other road users. Brake failure can result in death. If you are unsure of your mechanical abilities, please do not attempt this repair.
I developed this method from a vague hint on a motorcycle forum as to what the problem might be. I hope you find it useful.