Electrolysis is the fast lane of coin cleaning. What can easily take months with olive oil you can do in minutes (seconds!) with this easily made contraption. Of course, with the extra power comes the risk of ruining your coin. Even with care you can end up with a slug on what was before a dirty coin with a lot of potential. Because electrolysis strips the patina of the coin you are taking a gamble that the core underneath is in good shape. Sometime the patina IS the coin.
First you need an old power adapter of between 6 and 12 volts. Higher voltages increase the risk of electrocution while not increasing the effectiveness of the cleaning process. You will need to clip off the plug end, separate the two wires and strip off the jacket down to the copper. Twist the wires and attach them to, if available, metal clips. For around $3 you can buy a dozen copper-plated micro alligator clips at Radio Shack..
Set it aside and get a shallow plastic bowl. Fill with water to a depth necessary to clean the coin you've selected and mix in salt. You don't need to actually measure out the salt... just put in a couple of spoons or so.
Plug the power supply in and keep the two clips away from each other. If they touch the adapter will short out and become useless. Dip the clips in the saltwater and note which one fizzes. This is the end that you will attach the coins to. On the other clip attach a piece of metal. To start, use something small and manageable like a key or spoon. Avoid copper or brass objects as these don't function very well.
You now have an electrolysis kit.
Stick both clips in now that they're attached and your coin should start fizzing. Depending on how crusted over your coin is, leave it in anywhere from half a minute to several. The coin should be fizzing vigorously. If it's less that's okay, it will just work slower. If you want the action to pick up just pour in more salt or get the two electrodes (the clips) closer together without actually touching.
Take the coin out and scrub it with a toothbrush dipped in some liquid soap. If you've left the coin in long enough the dirt should start coming off but chances are it'll need to go through another round of electrolysis. Very stubborn deposits may not yield to electrolysis at all and will need to be picked off with a knife or pick.
Lastly, you will notice that the water soon gets dirty. This is mostly not from the coin but rather the anode which is dissolving into the water. You will need to replace the water every so often and the anode, too, once it's worn away.