Turn your vacuum cleaner off and unplug it. Flip the vacuum over so you can see the agitator brush. Unscrew the plate covering the brush and remove it. Remove the agitator brush by lifting it from the two slots that are holding it in place on each side.
If the old belt is still there (a broken belt may have already fallen off), slip it off the agitator brush and the drive shaft. Put all of your parts in one place so they won't get lost, excluding the belt.
Write down the make and model of the vacuum cleaner. Take the belt and the vacuum information to the place where you purchased it, a hardware store or a vacuum cleaner shop and get a replacement belt. Most belts aren't expensive and come two to a package.
Clean out any hair or other debris from the agitator brush and inside the area that holds the belt and brush before installing the new belt. You may have to use a pair of scissors or a knife to cut away any hair that's wrapped around the brush. This will allow the brush to do its job better.
Slip the new belt onto the drive shaft and the agitator brush, reversing the steps you took to remove it. Since this is a new belt and it might be stiff, you'll probably have to stretch it to fit the agitator brush back into the slots it came out of. Screw the cover plate back on, and the vacuum is again ready to use.