Setup your electrolysis unit near a source of water and preferably somewhere that there is fresh air, no sense in breathing in any more fumes than necessary.  I have found that the electrolytic solution becomes somewhat corrosive after use, so I recommend placing your zapper on something that you don't care about.  I don't recommend using it directly on the kitchen counter, as the other half may not appreciate a ruined counter.

Next fill up your container with electrolyte solution, I recommend baking soda, but you can experiment with salt as well.  Make sure that a good portion of the anode is covered with the solution, but don't let the solution touch the connecting lead that goes to the positive terminal of your source.

No matter how big your zapper is or how many coins you do at one time, getting the polarity correct is very important.  The coin goes on the negative lead and the piece of metal (anode) on the positive lead.  Once you have the leads connected place the coin in the electrolyte ( I like to leave the coin suspended).  Make sure that the coin is not touching the anode, this will short circuit the power supply and could ruin it..  Once the coin is in place, turn on the power supply.  This will vary with different supplies, but most likely will mean plugging the supply into the wall outlet.

After the power supply is plugged in you should see bubbles start to form on the coin and the clip, if the bubbles are forming on the anode the leads are backwards.  Unplug the adapter and switch the leads around, then plug it in and see if the coin bubbles.

If you see bubbles forming on the coin you have started the electrolysis process.  Good job!

The time that is takes to clean the coin is variable and depends on how the dirty the coin is, what the encrustations are and how much current you put through the coin.  What I recommend doing is checking your coin at regular intervals.  Don't forget to disconnect the power supply, then take out the coin and give it a brushing while running it under tap water.  The coin can also be checked by lightly scraping at it with a brass poker or a sharpened bamboo stick.

If you are lucky and everything works out, you will be able to save the coins patina.  But most of the time the coins patina will be removed or partly removed.  If this happens you can put the patina back on the coin.

As with most things in life, the more you zap coins the better you will get.