I've been using electrolysis for about 20 years now. It's super simple and the others above have posted all you need.
Just remember the DC (direct current) power source has two wires. One is negative and the other positive. Make sure you get the negative to the coin. The current will then flow from the coin to the stainless steel spoon.
Always use a stainless spoon, never any other metal. Other metals will discolor the coin.
So use a car battery charger, computer power supply, or whatever. You can often find these at thrift shops for 50 cents to $1.
If possible, buy stainless steel clips to hold the coin or whatever.
BAD SIDE: Too much electrolysis can ruin a coin or artifact. I've found that exposure to it for too long can eat away coin detail and it will weaken metal (makes it brittle).
Electrolysis is THE GREAT REVEALER. It reveals the true condition of any metal object.
It's only to be used when all other methods fail.
It should only be used long enough to bring out enough detail to attribute the coin or artifact.
It's one of many methods. It's not the whole ballgame.
Badger P.S. I've got a badly corroded iron relic in electrolysis at this very moment.