I am just a high schooler, but I have been doing this reaction for years without incident.
Thermite is basically a mixture of iron oxide (rust) powder and aluminum powder. Basically, during the reaction, the aluminum takes the oxygen from the rust and we end up with molten iron and aluminum oxide in a primitive single replacement reaction. The reaction usually produces enough heat to reach temperatures in excess of 2000 degrees F, which is enough to melt sand into glass.
Unfortunately, thermite requires a very high temperature in order to ignite. Usually magnesium is burnt on top of the thermite to start the reaction.
1. Getting the materials.
==== Rust powder is the easiest to get. One method is to drag several high-strengh magnets along the beach. This will pick up numerous small peices of rust, which can easily be broken up with a hammer to make powdered iron oxice.
An alternative method if you do not have a nearby beach is to place a lot of steel wool in a large bin of salt water for a few weeks and then filter out the salt and grind up the remaining powder.
When in doubt, just buy Ferric oxide from my link.
==== Aluminum powder is where it gets harder. One possible way is to take apart an etch-a-sketch. These rely on Al powder to make the designs.
Another way is to file down a brick of aluminum, or grind up aluminum foil in a blender. I do not recommend either of these.
Some paint stores sell aluminum powder for glossing paint. You may get lucky if you call around.
I personally would just buy the powder from my link. It is far cheaper than buying it from a non-chemical supply store.
==== Magnesium is fairly hard to obtain also. The reason that it is used to light thermite is because it burns with a striking white light that produces enough heat to trigger the reaction. This is another thing that I would recommend buying (make sure that it is either a ribbon or a powder when you buy it, as it will only burn in these states.), but if you really want to find your own, look for fireworks that burn with a “cool white” color, as these usually have magnesium in them. Possible sources include sparklers, strobe fireworks, and road flares.
2. Making the thermite
Mix the aluminum and the iron together in a plastic container in a ratio of 3 parts aluminum to 5 parts iron oxide. Mix the powders very well, and do not store the mixture for an extended period of time.
If you bought magnesium ribbon from my link, cut off about six inches and cut it into thin shreds. Cut off another six inches and keep it intact. Store these separate from the thermite.
3. Preparing for the reaction.
Find clay flowerpot to house the reaction. Do not use any other type of container unless it is solid clay, as most materials will melt under the tremendous heat of the reaction and cause the reaction to explode. Put aluminum foil over the hole in the bottom of the pot (if it has a hole) so that the thermite will not fall out. Again, do not use any other material, lest you have an explosion.
Put the thermite into the pot, and make sure that it is fairly level. Make a small indentation in the top of the powder and put the magnesium shreds in it. Do put the full strip in yet.
4. Summon the Hellfire
Clear an area with a ten foot radius and with no nearby houses. Place the pot in the center.
Light the six-inch magnesium strip (this may take a minute or two, so use a lighter) and put it into the pile of shreds on the thermite, making sure that the flame is touching the shreds to ignite them. If you are using a firework instead of magnesium, light it and place it so that the top of the flame reaches the thermite.
Get thirty feet away (just in case it explodes). You should see the initial flash of the magnesium, followed by a pause, and then a sudden burst of fire as the thermite reacts. Once the reaction is complete, molten iron will be left in the pot, and so avoid the pot for at least thirty minutes after the reaction to avoid being caught in a sudden explosion.
Do not ever try to extinguish this reaction or mix things into it. This will invariably lead to an explosion, which can easily kill you.