Newer flash guns have radio triggers built in and of course there are a lot of flash triggers out there, I use these triggers when underground, they are cheap and light weight:
http://r.ebay.com/8Vg2Xl
There are also the dedicated caving triggers -
http://www.fireflyelectronics.co.uk/pages/info.htm - but these days these are quite expensive for what they are. Other than th0se fireflies I'd avoid light based triggers and go for radio ones, like the ones I linked. The firefly is really sensitive to IR light from the flash, the cheaper optical triggers aren't that sensitive and you often want to tuck them down behind a rock of what ever.
You cannot use the on camera flash at all because it will light-up the mist in the air and your photo will look foggy, all your flashes need to be off-camera. If your camera doesn't have a hot-shoe or flash cable socket, you need really need something like the firefly to trigger the flash.
The difficulty with
@Phil V 's suggestion is moving around the cave without creating unwanted light from your head torch, although some people make it work.
Edit to add, flashes have different powers so it hard to say how far they will reach, remember that most cave photos are shot wide angle so things look further away than they are. Unless you get some pretty heavy duty kit you can probably only do 5m to 10m, also limestone and mud are a variety of shades of grey and brown so absorb differing amounts of light.
