Anchored or Drifting with Bait or Jigs:
This is easiest. I have to assume that you already at least know the basics. Some fishermen use drogues to reduce their drift, you can also slow your drift some by dangling your feet in the water. If you start getting uncomfortable, you can also swing both legs over the same side and sit "side-saddle" if you can balance and are comfortable that way.
Trolling takes a little experimentation and practice. You will have to experiment a bit to decide where you want to set your rod while you paddle-troll. I used to just wedge the rod butt under my knee with the tip extending out beside and slightly aft of the seat. It worked ok but wasn't really convenient and was pretty rough on rods. It took some experimentation to find a way to mount a rod holder so that while I was trolling, the line and rod didn't interfere with the paddle
Some fishermen prefer to use rod holders mounted behind the cockpit. They are definitely out of the way there. You will probably want a drag that makes enough noise so you will know when to drop the paddle and grab the rod.
I like to mount the rod holder up near my feet. The Rod is beyond the normal swing of my paddle. The line runs straight back over my head and doesn't foul with the paddle even while turning. The tip is held high and out of the way but I can still see when the rod starts jumping and easily reach the rod to reel ‘em in. Depending on where you are able to mount a rod holder on your kayak, you may have to scoot forward and out of the seat to reach the rod.
Depending on what I am trolling with, I will either cast out or drop enough line so that the lure reaches well into the water. I often begin paddling backward and let twenty or thirty feet of line out before I turn the boat in the direction I'm going to troll. Then I set the drag very lightly so that the movement of the boat is enough to pull out line. When I'm satisfied I've let out enough line, I tighten the drag just enough to hold it from pulling out further. I change my trolling speed from time to time, make wide and short turns, whatever it takes to excite the fish.
When a fish strikes on the troll you can drop the paddle in the water if it is on a leash or slide it under your leg or a gear strap. Wait until the fish is really spent if you are going to and land it. If you are using a net, hold the rod high with one hand and slide a net under the fish. I often dispense with the net if I can get a hold of the gills. Of course, if the line is strong enough, you can lift small fish aboard by the line. I would hesitate to use a gaff from a kayak but if you want to try it, that is up to you.
You should have a bag or stringer handy to transfer the fish to immediately when, or even before, you unhook it. It is just a short jump and he'll flip right out of the kayak. Take a cotton rag along so you can wipe fish slime off of your hands.
Casting lures, flies or bait:
You shouldn't expect to make very long casts while seated in a kayak but don't let that stop you. You may be able to get much closer to the fish with a kayak than you would by wading or with a powerboat.
If you are using heavier line, don't expect that you can just haul back hard on the rod and break it. If you try this, you will likely just flip the boat. If you can't work the snag loose, try wrapping the line on a cleat or something on the side of the boat. Let the swells provide the pulling force or paddle away to bring the line tight. Don't go out in a kayak with very heavy line or you might regret it.
The Special Thrill of Kayak Fishing
Is a fish big enough fish to give you a sleigh ride. You will have to hold the rod tip near the bow to get much of a ride, even from a large fish. If you hold the rod tip out to the side, the lateral resistance of the hull will probably prevent the fish from pulling you very fast.
I once watched a demonstration of how the Greenland Kayakers would manage the pull of a harpooned seal. The demonstrator had a dozen guys take a line and try, tug a war style, and pull as if they were the seal. The paddler tied the line to the boat, stuck his paddle in the water and laid the kayak over on its side. The lateral resistance of the kayak and paddle blade made it very difficult to pull him.