Vinyl siding is (most of the time) pretty easy to replace, assuming you can locate the manufacturer of your existing siding, and assuming that your existing siding isn't so old and weathered that there is no way to match it with a new piece.
Most vinyl siding has a nailer section on the top, and the bottom of the piece "snaps" over the top of the piece below it. To get a piece of siding off, just take a putty knife, or my favorite, a painter's 5-1, and pry the bottom of the piece you want to remove away from the piece below it.
Next, remove the bottom of the piece above to expose the nails of the piece you want to remove, and pull the piece off. Remove the old nails, place the new piece, cut to the right length, where the old one was, hooking the bottom over the top of the piece below it, and use ZINC coated broad head nails (roofing nails work well, they should be at least an inch long) to nail the new piece in.
Now, spray some Windex on the tops of the new piece to lubricate it, and pry the bottom of the piece above down over the top of the new piece. Done!