This method, sometimes called the potato press, is a cheap and easy way to do basic symbols or lettering.
Buy a bag of raw potatoes. One potato can make 2 letters or symbols, so if your band is "Organ Blues" then you will only need five potatoes. Cut the potatoes in half.
Using a pencil or marking draw out an individual letter on the flat side of the potato.
Using a knife, carefully carve away the surface area surrounding the letter or symbol so that it is elevated about a 1/4 to 1/2 of an inch.
Pour a small amount of textile ink into an old coffee can lid or any container with a small lip. Textile ink can be purchased at most art supply stores.
Put some newspaper inside the t-shirt, so that excess ink does not bleed through to the back, and lay it on a hard, flat surface.
Dip your potato stamp into the ink so that only the carved letter or symbol is coated evenly.
Firmly press the stamp into the shirt for a few seconds, using a ruler to keep everything straight. Make sure that the letter comes out as evenly as possible. Repeat this process with the rest of the letters then allow the shirt to dry completely.
This is pretty basic, but it works and allows for variations in color, layout and pattern.
For more complex designs, screen printing is your best bet. You can buy pre-made screens from some art stores, screen printing companies or online. They are also not hard to build. You'll need a nylon screen with a 1/10 mesh. Then build a wooden frame with the screen glued or stapled to one side. Sizes can vary, but 2 x 2 feet is plenty. You will also need to buy a scoop coater, photo emulsion and textile ink.
Draw out your logo, design, band name, whatever you want on a piece of paper. It's best to scan it into your computer and use Photoshop so you can play around with it and make the color consistent. Then print out the design on a transparency. Kinkos also provides this service.
Go into a dimly lit bathroom or basement because photo emulsion is sensitive to light. Pour about 1/2 of an inch of the emulsion inside the nook of your scoop coater. Make sure that the emulsion is spread evenly across it.
On the front side of the screen, spread the emulsion with the scoop coater across the screen. Try to do this in one continuous scrape motion so the emulsion is spread evenly. Store the screen flat, in a dark space to dry.
Next, you are going to need a light source. This is the tricky part. You can use the sun, or other light sources from above, but there is going to be a lot of trial and error. The best bet is to build a light box so that the light source is below the screen. Experiment with different bulbs, but high wattage is best. The light box should be roughly the same size as your screen.
If you are using a light box with the light source coming from beneath the screen, then lay your printed off image on the bulbs and the screen on top of the box with the emulsion facing down.
If the light source is coming from above the screen, then you need to lay screen flat, with the emulsion side up. Then lay the image on the screen, but flip it over so that it will be going the right direction on your shirt.
Expose your rig to light for about 3 or 4 minutes.
After 3 or 4 minutes, remove your screen. You'll be able to see your image/logo burnt into the screen. Use a hose or shower head to wash the excess emulsion form the screen.
Lay the t-shirt on a hard flat surface. An ironing board is best so that you can pull the shirt over the tip of the board and no ink will get on the back of the shirt. Or you can simply put newspaper inside the shirt.
Lay the screen, face down on the shirt and pour some textile ink into the bottom of the screen. Use a squeegee to pull the ink over the screen. Then, in one pass, use some pressure to force the ink down through the mesh and onto your shirt. Allow the shirt to dry for a few hours.