In my high school and early college years, I worked with printing companies as a part time job. Most of the imprints we did used screens in some forms and it was always neat to see the process of getting images onto posters, glassware and clothing.
Turns out, you can do the exact same thing with clay. The above picture is a lovely example by Noella on Flickr and you can see the preceding steps here and here. Polyform offers a silkscreen kit which is a great basic starting deal. You can find it at craft stores like Michael’s. If you want more variety of silkscreens (and it’s like stamps and textures, you always want more) Etsy has a variety of great designs and kits.