The simplest and probably the most widely practiced method is to bash them on the head until they die.
The thing about that is, until you get used to it, most people tend to be too timid and end up brutilizing the fish.
Depending on the fish (some are umm.. hardier than others), you need a nice heavy object (called a "priest"), and its very important to hit that sucker as hard as possible on the first swing. swift and effective kill.
The other method, and the one I personally prefer, is to cut off the head straight away, that will both kill it, and provide a simpler method of gutting, it can also be bled easily that way (if need be).
If you cut the head off 90% of the way, and cut the belly open from the vent up to the chin, you can usually* just pull the head 'down' and the gills and guts will come out with it, you may have to do a little snipping around the gills and the back end, but its much nicer than pulling the guts out with your hands... the bigger the fish the more difficult this method is, and some fish are simply too lively to start cutting on straight away, in which case, refer to first method :)
No matter how you kill it, you should gut it immediately, and either cook it or start drying it as soon as possible. If you can't cook it right away, keep it as cool as possible. A bucket of seawater in the shade will be better than nothing. keep the fish whole (gutted) until you are ready to either cook or dry (or refigerate).
This is why most people TRY to catch smaller fish at sea, because you don't really want left overs and they are much easier to handle.
You could do some YouTube searches for fish killing/gutting techniques.
and here is a halfway decent blog about fishing from a sailboat. http://fishingundersail.blogspot.com/
Hey... didn't alex have a video of him gutting a fish while delivering a cape dory down the icw??? what happened to that?