In the old days screen printing stencils were hand cut with a razor blade and stencil material. Today artwork will pass through the digital realm before ending up as ink on substrate (read T-shirt or the like). The result is that screen printers are capable of acheiving astounding detail even on rough surfaces like T-shirts.

Multi-colored artwork needs to be separated into single componant colors in order to be printed. An image of the isolated color is printed on a transparent film which is then used to expose a finely-meshed screen coated with a photosensitive emulsion.
Films for a three-color print

One screen needs to be made for each color used in the artwork. After precision mechanical allignment each color ink is forced through it's screen onto the item to be printed. Using proper techniques the illusion of many colors can be made with only a few actual ink colors!

How many colors do you see? We used four ink colors.

Intense light is shined through the film onto the printing screen thereby hardening the emulsion. Unexposed areas of the screen created by the dark areas of the film are then washed out with water leaving clear areas in the mesh that ink can pass through.
Printing screen being exposed

Unexposed image being washed out of screen

On dark shirts colors may need to be underbased so that the colors are bright. This may mean that an extra screen needs to be made.
A Navy Blue shirt without underbase and with an underbase print.