Director George H. Burgess of The Florida Museum of Natural History has written up suggestions for divers encountering aggressive sharks that lend some helpful insights to kayakers so I have integrated them here.
If you see a shark from your kayak, do not panic. Most likely the shark was attracted by something you were doing or by something in the area of your activity. If you are fishing and have a bait bucket over the side, let it go. If you think some catch of yours is attracting him, let him have it.
Regardless of the reason for its attraction do what you can to eliminate it and calmly start toward shore, keeping your eye on him, paddling with smooth gliding strokes, not frantic splashing. Gather up close to a paddle buddy as sharks are less likely to go after a group. Stay in your kayak until you reach shore. If you are far from a landing try to get up against a cliff (in calm water of course) or wall to minimize the directions he can approach you from.
Should the shark be making aggressive advances toward the boat, your paddle is the best weapon to discourage him. Hitting him on the snout should work but if he comes back go for the sensitive gill or eye area. I've wondered why I can't find expert advice on hitting them in the gills or eye to begin with. My conclusion is you do not want to assault a shark just because it is curious. The snout bump let's him know you are not helpless. Sharks are scavengers often looking for an easy meal like sleeping fish as a midnight snack so playing dead doesn't work here. Let him know you have a paddle and know how to use it, but like he and most creatures of nature do, showing ability to do battle is safer than an actual battle for all concerned.
If he knocks you out of your kayak, hold onto your paddle with all your might. Leap back onto your boat and swiftly, not frantically, paddle into shore. If you lose your paddle or kayak, swiftly, smoothly swim to another kayak or to shore. Let the kayak find its own way in if necessary. If you can't get to shore find a way to back up against something to again, limit the directions he can approach you from...and again, don't play dead. Use your hand to bump his snout if you lost your paddle. Leaping onto your kayak swiftly, quickly, even effortlessly, from deep water is achievable and an invaluable skill all sit on top kayakers should aspire to master.
Thanks to TopKayaker.net
This You Tube video is strickly for your viewing---is not related to the above story!!!