You design a t-shirt with design programs like Adobe Illustrator and Photoshop. Then you learn how to separate the colors by layer, and send the file off to a screen-printing company. You can't do it yourself and it's not cheap. Usually you have to buy the shirts, the screen, shipping and labor fees. Most companies won't print for you unless you print in bulk. Good luck!
American Apparel shirts are amazing. And they ship in bulk, which is cheaper than buying them normally.