Use a zip tool (Image 1) to unlock the siding from the surrounding pieces (Image 2). Start at the bottom of the piece that is being replaced, and insert a wooden shim between the pieces of siding as the zip tool slides along the siding. Repeat the procedure for the top of the damaged siding.
Use tin snips to cut out the damaged area (Image 1). Use a table saw or circular saw to cut a patch from a good piece of vinyl. The patch should be larger than the piece you removed.
Run a bead of adhesive caulk around the back of the patch, and set the patch in place (top image). Then lock the siding back into place.