This Instructable covers the standard photo-emulsion screen printing process, which is great for printing text or images with fine detail...and at the end, you have your own personally-designed entirely unique prints on fabric, clothing, paper, or whatever else you can get under your screen.
The general idea: After stretching fine-mesh cloth over a wooden frame, you spread a thin layer of photosensitive emulsion on the screen and let it dry. You then take a black image on transparent or translucent surface, place it against the screen, and then expose the screen to light. The light causes the emulsion to harden and bind to the fabric. Where the light strikes the screen, the emulsion will bind, making a solid layer. Where the light is blocked (ie where your black image is placed) the emulsion remains water-soluble. After exposing the screen, you spray down the screen with water, washing off the emulsion only where your image was placed; this clear area is where ink will be pressed through the screen when you print. Finally, you lay the screen on your t-shirt, other fabric, or paper, spread ink on the inside of the screen, and press the ink through the screen. If you use textile ink, you can heat-set the ink after it dries, and it'll be permanent and washable.
There are some great Instructables up on the site already for screen printing methods, but there's always room for more. For this project, I went with a ready-made screen and images printed in black on transparencies.
Check out Screen Printing: Cheap, Dirty, and At Home for info on making your own screens and using the sun to expose your photo-emulsion.
Threadbanger has an excellent D.I.Y Screen Printing Instructable which covers making screens using old embroidery hoops and using Mod Podge to put your image on the screen.
How to Silk Screen has a good overview of the photo-emulsion process.