Hydrogen Gas
To generate hydrogen, all you need is an acid and a metal that will react with that acid. Try vinegar (acetic acid) with zinc, aluminum, magnesium, etc. You can collect hydrogen in something if you note that it is lighter than air.... light a small amount and it burns with a small pop.
Another way of creating hydrogen is by the electrolysis of water. this involve sseperating water (H2O) into hydrogen and oxygen by an electric current. To do this, you need a 6-12 volt battery (or a DC transformer), two test tubes, a large bowl, two carbon electrodes (take them out of an unworking 6-12 volt battery), and table salt. Dissolve the salt in a large bowl full of water. Submerge the two test tubes in the water and put the electrodes inside them, with the mouth of the tube aiming down. Connect the battery to some wire going down to the electrodes.
This will work for a while, but chlorine will be generated along with the oxygen which will corrode your copper wires leading to the carbon electrodes... (the table salt is broken up into chlorine and sodium ions, the chlorine comes off as a gas with oxygen while sodium reacts with the water to form sodium hydroxide....). therefore, if you can get your hands on some sulfuric acid, use it instead. it will not affect the reaction other than making the water conduct electricity.
WARNING: DO NOT use a transformer that outputs AC current! Not only is AC inherently more dangerous than DC, it also produces both Hydrogen and Oxygen at each electrode.
Take the test tube of hydrogen and cover the mouth with your thumb. Keep it inverted, and bring it near the bottle of chlorine (not one that has reacted with turpentine). Say "goodbye test tube", and drop it into the bottle. The hydrogen and chlorine should react and possibly explode (depending on purity and amount of each gas). An interesting thing about this is they will not react if it is dark and no heat or other energy is around. When a light is turned on, enough energy is present to cause them to react...
Get some hydrogen peroxide (from a drug store) and manganese dioxide (from a battery- it's a black powder). Mix the two in a bottle, and they give off oxygen. If the bottle is stoppered, pressure will build up and shoot it off.
Try lighting a wood splint and sticking it (when only glowing) into the bottle. The oxygen will make it burst into flame. The oxygen will allow things to burn better...