Lots of fine advice in this thread. Let me add something I haven't seen exactly: ways to get over your"Mammalian Complex" and/or fear of the water.
Long post coming, but it works and is fun to practice. It comes from teaching dudes to stay cool and survive on and under water. The posters who said to mess around under water are right, but consider taking it further which can really cement a feeling of comfort underwater (oops!).
I'd suggest you have a few sessions in SCUBA to at least the point where you can hover on your head,then on your back staring at the surface. Be sure you're with a certified, well-experienced instructor. Tell him/her you're not wanting to get a dive ticket (unless you are), you just want enough underwater time to begin feeling like it was no big deal. Also, practice going to the bottom of the pool, adjusting your buoyancy to neutral then just hanging out trying not to move, except for slow breathing. Feel yourself become one wit the water.
When you get that down, have the instructor teach you how to doff and don your mask while at the bottom of the pool (not snorting water up your nose--breath control. When ghat becomes easy, ask if he/she would let you try and don all your gear underwater. That's where everything is dumped overboard and left on the pool bottom and you have to jump in from the deck and put it all back on.
By now you should be getting a little more water-friendly, so try this: without mask snorkle, air, or weights, jump in and do a few very slow barrel rolls and somersaults. When you get OK with these how about trying some just plain floating on our back for 10-15 minutes at a time. good lifegurd or SUBA dude can show you the tricks to that. (mainly it's just a matter of staying calm. You're not gong to sink, and this is where you'll begin to trust that (unless you're one of the unfortunates who is naturally negatively buoyant.
When you get to where 10-15 minutes is cake, it's time for drown proofing and this is where you'll really learn to trust yourself and the laws of physics. When you do ll of these exercises be sure the lifeguard is aware of what and why you're having so much fun playing squid.
Drownproofing is just another kind of floating except ou do it vertical, not horizontal like a traditional float. Go to the deep end of the pool, as far away as possible from others so they don't toss you on your ear. Tread water very gently and just with our arms and hands. Calm yourself. Focus on your gentle breathing and gentle hand movements. Begin to slow it all down and as you do, slowly move your hands to where you can grasp them behind your back, arching your back gently, especially your upper back and take s slow, deep breath and hold it.
Next see if you can hang out in that position for a slow count of 15, then begin to slowly exhale through your mouth (later when you get really good, use just your nose.). Keep your body still as you feel yourself beginning to lose buoyancy and descend. Before your mouth goes below the surface, take a deep breath and hold it as your body (now positive) begins to rise slowly. Hold yourself still! Still your mind. Put a lid on any panic. Just fins a quiet spot in side and hold there until you repeat the cycle. Repeat until where you can do this for 10-15 minutes and love every minute. By then you'll have begun to feel relaxed underwater.
Now, any practice you do underwater seated in your boat, will be more meaningful since you will have begun to learn the water can be your friend. So friendly that your goal ought to be to make the above he most incredibly relaxing meditation you can imagine.
Unless you're out of the average for any reason, you an get a good handle on all the above in 2-4 hours of pool time. At, sya. $8-$12/ hr.pool time plus the SCUBA time, it is hugely worth it. because no you're ready for the nest step.
Practicing swimming in a river and becoming good at both defensive and offensive swimming. Please work with a qualified kayak or safety teacher on this, an while you're at it get in some rope practice as well. Now you're confidence is so up there your roll will likely become ankiety-free.
Practice being a squid every so often, specially in the off-season. Only downside to squidage is pruneskin. But its worth it. Consider using goggles to keep the chlorine at bay. But not noseplugs or ear plugs, yes, nose plugs in a kayak are a must, IMO, and can help you in the early phases of learning the above, but the goal is to become so aware of your breathing and body/mind, you won't and such a pro that when/if you snort water it's no big deal at all. You might find it interesting to read up on Sinus Reflex and how to control & deal with it. Point is: n a kayak, you're playing in the waterworld so embrace it. More fun that way! And the after-beers taste a lot better,
HTH and roll well.