I did not know this until BlimpEnthusiast told me this in the comments: "Great electrolysis setup! In my electrolyzer I use baking soda as the electrolyte. Watch out for the chlorine gas that comes from the positive electrode when using salt and be in a well-ventilated area." Baking soda produces harmless CO2.
So I now recommend using baking soda instead of salt as the electrolyte.

Step 1: Hydrogen and Oxygen From Water

Electrolysis is the process of using electricity to make chemical changes in a substance. When you pass electricity though water to split the hydrogen and oxygen atoms you are using electrolysis. The electrons passing through the water between the electrodes split the water molecules and the hydrogen atoms travel to the negative electrode and the oxygen atoms travel to the positive electrode. What I do in this Instructable is put a jar over the negative electrode to capture the hydrogen that bubbles up. What I did to make this Instructable unique from the hundreds of other Instructables about electrolysis is that instead of using a battery to power the electrolysis I used a 6 volt wall adaptor. To minimize risk of electrocution I made sure there was a drip loop between the water source and the outlet.

Step 2: Power Source

For the power source I used a wall adaptor that had just 2 separate wires and with a easily identified negative wire. In this instructable the negative wire is the one with the white stripe along the side. Next I cut off the connector so it would no longer be able to to whatever device it was for and then split stripped the ends of each piece if wire no more then a inch. Next I wrapped aluminum foil around the 1 inch long pieces of exposed wire. This is to protect the wires from the water and decaying effects of electrolysis, as well as to make a larger surface area for the electrodes to give them better energy efficiency.

Step 3: Assembly

Next I found a small tray and filled it up with about 2 inches of water. Now I took the positive electrode and put it into the tray off to the side and taped it there with a little scotch tape. Now I got a water bottle lid and cut a small groove in it. This so it can hold the jar up a little bit to make room for the negative electrodes wire and water to have a path from under the jar to the negative electrode. The groove is so it doesn't slip out from under the jar. Next I fill the jar as full as I can with water. After that I put about a tablespoon of salt in the pan and jar. This is because water doesn't conduct electricity well unless it has impurities in it. Now I put the lid on that jar and stick it in upside down in the water. Now keeping the lip of the jar under water I take of the lid. After this I take the water bottle cap and slip it under the jar so there is a crack between the jar and the bottom of the tray. Next I take the negative electrode and slip it under the jar so all of the metal is under the lip. If any is outside of the lip the hydrogen that accumulates there will float up outside of the jar and go into the air where it will turn back into water.

Step 4: Final Steps

Now all you have to do is plug in the adaptor. Make sure there is a drip loop between the pan and the adaptor so that water doesn't reach the outlet. Now all you have to do is wait for the hydrogen to start collecting in the jar. The hydrogen "should" be slightly compressed because it pushing out the water already in the jar but I am not certain. The first picture shows how much hydrogen had collected in a couple hours and the second one shows how much collected overnight. The third picture shows what it looked like when it was full of hydrogen. My electrolysis is not fast or efficient but it uses a outlet instead of a battery like so many others so power and time don't matter very much. I hope you enjoyed this Instructable and and if you improve on it or create a better one please show a picture of it in the comments.
Here is a link to a YouTube video I made of lighting the hydrogen on fire. (The fun part)
http://youtu.be/vU4mNuSb8Gs
Remember to wear eye protection even though it is unlikely "Blow up" or anything major.