If you suspect that your zipper is a bit worn down, apply a thin coat or two of clear nail polish to the teeth of your zipper. This may restore enough of the shape of the zipper teeth to become functional again.
If the zipper still functions but is very hard to close, use petroleum jelly as a lubricating agent to allow the zipper to slide more easily. However, apply it gently, as too much jelly will cause more problems.
A pencil is another great tool for stuck zippers, as the graphite found in its lead works as a lubricating agent that should allow your zipper easier movement. Just make sure your pencil has a decent amount of lead, then rub it gently over the zipper's teeth.
If there are pieces of fiber wrapped around the zipper's teeth, grab a pair of tweezers and try to gently pull out any fibers or other particles stuck in the zipper. Once removed, it should be sliding smoothly again.
If you find your zipper slider isn't staying on the track, start at the bottom of the zipper and begin to feed those rogue teeth into the slider manually. A basic screwdriver can help squeeze those zipper teeth back into their proper position and get your zipper working again.