Ahhh the beauty of Home made Rockets

Required Ingredients

A type 3 fire extinguisher. Do not screw around with this. Water won't cut it.
Eye protection.
Aluminum foil
Black Powder (FFG burns slower, FFFG burns faster, start with FFG). If you're having trouble finding black powder, you can buy it online but will have to pay extra for shipping.
Fuse material
A wide open field
Long, straight sticks

For larger rockets only:

PVC pipe or any lightweight tube
Skewers from the supermarket for making a center channel in your propellant. (Prep these by covering them in wax if they are porous).


A road flare (color)
Iron filings (color, smoke)
Flour (smoke)
Clumping kitty litter (packing)
Plastic bag with string (parachute)
The only hard part to find is the black powder. You need to find FFG black powder and only FFG black powder. When you feel confident with FFG and actually have a few successful launches, you can start using FFFG. FFFG burns much faster and requires better rocket design, so start with FFG. Do not use smokeless powder, pyrodex, 'black powder gel' or pellets. You may use pellets in small rockets only. Smokeless powder burns far too quickly and you will have an awesome explosion (but this might be what you want for the finale). Pyrodex does not absorb water and does not pack well. Black powder gel is just weird and doesn't work consistently. Pellets work only in smaller rockets.
Fusing material can be just about anything with a consistent burn rate. Keep in mind that the fuses really should burn in the absence of oxygen which means either legitimate fuses or you can take a string and roll it around in the blackpowder. You always need to test whatever fusing material you have for both burn rate and suitability. To test for burn rate, prep your fusing material and cut a 1ft length of it. Set one end on fire. You need however much material takes 10 seconds to burn to give you plenty of time to run away. You should always assume your rocket is going to be a colossal failure and explode on the ground. The next test will be to take fusing material you're happy with and take a small piece of foil about an inch long. Fold it over and take a pair of pliers and clamp it down hard over your fuse. Your fuse should burn from one end of the other of the foil without snuffing out. Does that work? Great, you have something you can use for rockets.

If all else fails, try a stick of incense you can buy at a head shop or ask the sporting goods store you bought your blackpowder from if they also carry match-lock supplies. You can use sparklers for larger rockets, their metal rod also makes a decent prop for your rocket but may be too heavy for smaller rockets and poppers.

Small Rockets

These are the most fun for small poppers and let you get a good grasp of the concepts.

Take your aluminum foil and pull out about a 3 inch wide strip across.
Fold the strip over three times (1 inch strip).
Put a pea-sized ball of blackpowder into a detent on one size of the foil. Cut a small bit of fuse (enough time to get your hand away) and make sure it lies in the powder to the top of the ball. You can experiment with this, putting the fuse to the bottom of the ball results in a longer but less powerful burn. Putting it more toward the top results in a quicker, more powerful burn.
Roll the ball and fuse up in the foil.
Using your pliers, fold over and crimp the top of the popper as hard as you can. Crimp the bottom also but don't fold it over. You've now made something which you can light and will spin on the ground. Try crimping the fuse to one side.
To make a rocket: Tape the popper fuse down to a long straight stick. Usually your local supermarket will sell skewers for BBQing, the thinnest ones are best. You can also use spaghetti on the small rockets, it only needs to hold it upright long enough for launch.
You can either launch this by sticking the stick into the ground but it's much easier to use a soda-can or bottle. Put the stick in the mouth of the bottle (jet pointed out the mouth of the can or bottle) and light it. The little foil popper will go screaming off. Try twisting the crimps to make fins for your rocket!
Large Rockets
The secret to large rockets is getting the propellant packing to work. The easiest packing is simply pouring black powder into a tube and tamping it down either with a smaller tube or a wooden ram. Pack by hand, the diameter of the tubes doesn't have to mate exactly. Faster rockets have a hollow channel in the center but are harder to pack.

To get the mix right, take a small portion of your blackpowder and mist it with water. Using your fingers (being careful about static and open flame), try to form a ball with the powder. Once you can form a ball and the powder is sticky, you have about the right amount of water. Right now the powder won't fire and if you let it dry over night, it should retain its shape. After you let it dry, it will fire, and you must treat it with respect. If you're having trouble getting your powder to clump (keep in mind that powder is generally designed for use in firearms and not for rockets, it may be coated in wax or other chemicals), add very small amounts of clumping kitty litter until it does hold it's shape. Make notes of the ratios of litter/water/powder for particular brands of powder and litter. The more litter you use, the less evenly the powder will burn, the less reliable your engines will be. Use the litter sparingly. You can use your test balls to make small poppers or rockets, which will also give you a decent idea how well it burns.

Wash your hands thoroughly after handling powder.

Building the Tube

Take your PVC tube. The reason why we're using PVC is because it's rigid, forgiving to accidents in packing (usually a hole burns in the side before the pipe explodes), lightweight and easy to cut and drill. Do not use glass bottles ever or metal pipes until you're more familiar with powder. Try to find thin walled PVC without threads. At minimum, it should be 1:3 (one inch inner diameter to 3 inches tall) and after 1:5 the rockets seem to nose over.
Take your aluminum foil and roll it three times (or four or five) over the outside of your packing dowel. Slip it inside of the PVC tube. This provides insulation against the heat of the engine. Use your packing dowel to roll the foil against the inside of the PVC pipe. You might try using double-sided tape on the inside of the tube at the top and bottom to give the foil something to hold onto. Air-gaps will result in the foil trying to expand inside the tube and tearing in flight which will cause your tube to explode or wander. Do a good job here or don't do it at all and pray your tube is thick enough to put up with the propellant. It won't be, but the sulfur smell and burning plastic smell is sweet perfume to some of us. (If you find your rockets always explode at launch, you're either not using enough foil, you need to cut the powder more with your litter or did not pack the foil properly. Check to make sure you're using FFG powder and not FFFG which I have found is much harder to control).
If you're using a parachute, drill a hole in the "top" of your rocket through the foil. Tie the string through the hole and fashion a parachute out of your plastic bag. Use an equal length of string to your rocket. If the rocket is 5 inches tall, use 5 inches of string. Take a very thin layer of clay, ball up the parachute (do not wrap the string around it, loose is better), and use the clay as a stopper between the tube and the parachute. You do not need a nose-cone. You need just enough clay to keep the parachute away from the propellant, so pack it thin. Turn the rocket nose (parachute) down and let the clay dry. Consider this part a learning exercise, the PVC gets cooked in a few launches but people generally don't like having PVC fall down in their neighborhoods. Use your head and use a parachute if your situation warrants it.
If you're making fireworks, skip the parachute and just cap it with as thin a layer of clay as you can pack. You can also cap it with foil, but I've found that you either need to rubber band the foil on and hope the charge is enough to burst it or just use clay since the clay becomes brittle.
A: For solid charge engines: With the tube "bottom up", pour blackpowder into the cavity. This is where the fun happens: If you're making fireworks, dope the blackpowder with flour for a trail or iron filings for color and light. (Iron filings which have rusted will also burn brightly and hotter, making more fuel for the engine). If you want, you can take a road flare and crush it. Putting the crushed flare in with the powder will make a tail for the rocket and packing it whole into the nose (before you pour any powder in) will make a brilliant burst of color when the engine burns through. The body of the rocket will still be carried upwards through the burst by inertia. Do not fill the rocket to the top with propellant, leave some space to build a clay nozzle. You want enough space to pack enough clay to make the rocket balanced or tail heavy.
B: For hollow charge engines: Using your water/litter/powder mix, drop the skewer into the clay at the 'nose' of the rocket. It helps if the clay is still a bit moist. The rod should be centered in the tube as much as possible. Pour your mixture into the body of the rocket and tamp it down with a smaller dowel that can fit between the hollowing rod and the body of the rocket. People who do this as a hobby actually have special tools with a center-drilled channel matching a rod but since we're just doing a small throwaway rocket here, just try to keep things uniform. Let it dry overnight. Do not fill the rocket to the top with propellant, leave some space to build a clay nozzle. You want enough space to pack enough clay to make the rocket balanced or tail heavy.
Take your clay and a dowel. Thicker is usually better. Push the dowel to the propellant (or use the dowel you didn't pull if building center-channel propellant) and fill the bottom of the tube with a thick layer of clay. This provides two things: A nozzle and a counter-weight to keep the rocket pointed up. Don't be afraid to use too much clay as too little clay will cause the rocket to nose-over. Let this dry over night.
Push your fuse into the nozzle (this is where a sparkler works well).
You can launch there from a post in the ground taped to the side or come up with some kind of fins. Experiment!
Fun Things To Try:

How does the shape of the nozzle affect performance?
How open does the center channel of propellant need to be?
How open does the nozzle need to be for optimum velocity?
Try different mixes of FFG and FFFG blackpowder. How does adding rusted iron filings help the rocket?
What other items can be packed into the nose of the rocket to generate different effects?
What other materials will put up with the heat and force of the propellant?
How does putting a clay ball on the launching stick affect the flight of the rocket?
Nuntius contributed About.com's coloring fire and alternate smoke formulas.
HackerCracker suggested for yellow bursts, use sodium chloride (salt). For green, use barium nitrate from a chemical supply shop. For blue, use copper sulfate scraped from an old copper pipe. White is found in aluminum sulfate obtained from an old corroded aluminum pipe or pan. For a fuse, he suggests string soaked in potassium nitrate (saltpeter).
Remember, safety first. Keep the fire extinguisher handy. Make sure your fuses are long enough you can get a safe distance away. Make sure you have enough area that your rockets can come down safely.

Thanks to GhostofTiber for helping with this.