Unlike other meats, say chicken, fish in almost all cases has enough of it's own flavour and texture to stand alone after a quick flash in the pan. This technique is definitely best for smaller pieces of fish or fillets. Pan-frying a whole fish is probably not a great idea.
I always bang on about it, but a good frying pan is essential for successful pan-frying. A cheap and nasty, skinny pan is going to leave you with un-evenly cooked torn fish. So get a good non-stick heavy bottomed frying pan. I try not to put more than two pieces of fish in each pan, that way you keep the oil hot and avoid steaming/poaching the fish by accident.
Great fish for this method; salmon, tuna and other dense fish.
The Actual Cooking
A medium heat is probably all you need to avoid leathery fish caused by cooking too fast. Before the fish touches the pan make sure you dust with flour (to stop it sticking on immediate contact). Use a couple of tablespoons of rapeseed oil; add butter in the final 2 minutes of cooking.
The cooking will take anywhere between 2-7 minutes depending on how thick the meat is. Remember this tip here to make sure you're cooking just right!