Never kill an eel when you catch it. Wrap it in a damp cloth and keep alive in the bottom of the refridgerator until needed.
Kill by piercing the brain with a sharp impliment. See TIPS for correct technique. Or chop the head off using a heavy cleaver.
Stick a skeewer though the head and hang up.
Make two slits one on the dorsal side and one on the ventral side, from head to tail.
Work the skin lose using a knife then take hold of both ends and pull to remove the skin.
Slice open the ventral side and remove the guts.
Cut in to steaks and cook.
Experience the joys of an emergency tracheomtomy as you choke on a bone.