Built-in Self-timer - I think this method is unreliable and not very fish friendly as you have to leave the fish alone to mess with the camera. Sometimes the camera doesn't focus correctly either. The options to do more than one picture at a time is limited on many cameras.
Hand-held infra-red remote - I'm not keen on using these, they are sometimes a little fiddly. They work ok but I'd rather concentrate on holding the fish with nothing else in my hands. Sometimes a fin gets in the way too.
Wink/smile detection - some cameras have this facility now and it sounds perfect. It involves just winking or smiling at the camera to trigger the shutter. The truth is wink detection is unreliable in my experience. Perhaps I just don't wink well enough. Smile detection works most times but you can feel a little silly gurning at the camera by yourself. For both methods the camera has to be able to 'see' you so these functions are no good in low light or at night.
Wired guitar foot-pedal - if your camera can take a wired remote and you are good with electrics or know an electrician this is one of the best options. It requires buying a wired remote, cable to extend it, 2 stage micro-switch and a foot pedal wired in to replace the hand-held switch.
Air-release bulb - one of my two favoured methods now. Most modern digital cameras don't have a thread on the shutter button so a bracket needs to be purchased to position the air-release plunger over the shutter button. There are two sizes of bracket - one for small cameras and one for larger compacts. They don't fit some large SLR's like my Canon 600D. I had to modify mine by replacing the base with a longer piece of aluminium.
I find the most comfortable and practical place for the air-release bulb to be under the heel. Occasionally things don't work smoothly because the bulb fails to re-inflate or the ground is too soft and the bulb just squashes into the grass instead of triggering. (It usually works perfectly on the practice shots!) Generally speaking though this is a great method.
Wired programmable timer - I find I'm using this more and more and it is becoming my preferred method. They are about £15 on eBay, plug into the camera and have about a metre of cable. They plug into the cameras remote socket and the delay before starting, number of shots and interval between shots can be set individually. Eg. after 15 seconds take 20 shots, at 3 second intervals.
So lean over fish to press start, pick up fish, take the required amount of pictures, return fish. Delete the duff shots.
Depending on how well the fish behaves you can be done after half a dozen shots and you can either cancel the timer or leave it to finish while returning the fish.
Advantages of these are they are not seen in the pictures and hands and feet are free to do as you want so you can concentrate on the fish.
The interval between shots may need to be increased when using the flash to give it time to recharge. The interval also depends on how long the setting is for image review.
The connectors vary so be sure to buy the correct one for your camera.
I think that just about covers everything I have used in the past and currently use.
My camera of choice at the moment is a Canon EOS 600D SLR with a 18-55 mm f/3.5-5.6 IS II Lens.
This is very good for self-takes as it has a flip-around screen.
There are many other cameras with this screen function - mainly Canon models, some Panasonic Lumix and one or two other makes.