Game Bag   This is a must for every kayak angler. Unless you have a special fish bag that keeps the fish packed in ice, the game bag is your best bet.  Originally used by divers, the game bag has been adopted by kayak anglers to keep their fish safe and secure.  The game bag can be attached to an eyelet or a kayak strap.  It depends on which model and brand you have.  If your kayak has a tank well, the game bag will most likely reside there.  Some anglers  like to leave their game bag tied up, hung over the side (in the water).  This is fine if you're freshwater fishing.  If you're in the ocean, I would be a little more cautious about where and when you to do this.  You don't want to attract unwanted visitors.  If your game bag isn't too heavy, you can simply dunk the bag in the water and place it back in the tank well, in your hatch or on top of the kayak.  Some tank wells fill up with water enough to keep the fish in the bag moist.  You can actually use your game bag much like a net to land your fish.  Provided you don't have any fish in it at the time (follow the same steps for landing a fish with a net).  The great thing about using the game bag for storing your fish while you're out on the water is that most of the game bags have a latch to ensure you don't lose the fish after being bagged.  Fish have been known to jump clear out of bags and nets.  Put your fish inside, close the game bag and latch the bag secure.  With the bag securely fastened to the kayak, even a rough re-entry through the surf won't compromise your catch of the day.

Net   Though self explanatory, netting fish can still require practice and skill.   If you are planning to release the fish,  take extra care when netting.   If you are planning to keep the fish for consumption, the type of net is a mute point.  Most nets which aren't made of fine mesh can potentially do damage to the fish due to the wide webbing.  Try to take extra care when handling fish with the standard (wide webbing) kind of landing nets.  

A net is not absolutely necessary for landing fish.  It is a useful tool that can come in handy, and in many states, is required to be carried at all times.  Regulations will sometimes not only stipulate a net requirement, but also set a requirement for a minimum diameter of net size.  In California, the minimum net diameter stipulated by the Department of Fish & Game is 18 inches. When ready to net a fish, lower the net into the water, maintaining a vertical position with the net. With the other hand holding the rod, guide the fish into the net.  Hoist the net out of the water keeping it horizontal once the fish has been netted.