All you will require is a length of strong (about 20 lb.) nylon. For a small fly hook I've used 10lb successfully.
Double and loop the nylon around the exposed bend of the embedded hook. Then press down firmly on the hook eye, enlarging the wound channel and releasing the barb.
Pull smartly (snap it) on the nylon and the hook will come out painlessly, leaving only the original small prick in the skin.. There should be almost no bleeding.. Remember, the harder you press down, the easier the hook will come out.

I have removed literally hundreds of hooks over the years this way. The secret is to pull quickly and with a real fast jerk. Don't be afraid to pull and if a bit of brain comes with the hook then maybe you should have left it alone hahahaha.
I usually go "I'll count to three...... 1 snap !! oh sorry I can't count!! By the way practise on a piece of steak! not the dog as he can bite!