I work for Pamlico Sea Base ( http://pamlicoseabase.org ) as a sea kayaking guide. One of our trailers is built for canoes and doesn't have fenders over the tires. Unfortunately someone wasn't paying attention when loading it with kayaks and the sides of a few boats sat on the tire for a 2 hour trip. We now have 3 boats with gaping holes in them.
It isn't very likely that you'll have a kayak with such a large hole, but whatever the size, here's how to fix it.
Step 1: Materials and Tools
1. some sort of patch. we had an old trashed boat we could cut up. The only other plastic I know that will stick well are those big blue 50 gallon drum/barrels. Make sure you wash it out well!
3. heat gun (I used a blow torch which isn't great but works)
4. a water bottle (for safety reasons)
5. a large metal spoon or putty knife
6. a pair of pliers
Step 2: Prepping the kayak and the patch
Sand the edges of the patch and the edges of the hole. I used a grinder for the patch to make things go faster. (I had 3 boats with holes in them) Some people will tell you to sand the side of the patch that will stick to the boat and the plastic of the boat around the hole the patch with attach to. I don't know if this helps the patch stick or not because I didn't bother doing it. It's probably worth trying.
If the hole is next to the seat or any rigging or anything that would either get in the way or catch fire, remove it. For the boat pictured, we had to take the seat out, take the paddle holder off, and move the rudder cable.