The screen printing process is considered to be a relatively contemporary technique, but it actually dates back to the Chinese Song Dynasty (960–1279 AD).
Screen printing is called many things (Silk Screen, Serigraphy, Stencil Printing), but the concept and methodology are the same throughout, and very simple. In essence, screen printing relies on a few basic ingredient that together form a streamlined process. A permeable fabric mesh is stretched very tight (like a drum) over a rigid rectangular frame (like a picture frame), to create the "screen." A hard drying liquid called "emulsion" f(like glue) is then applied to certain areas of the mesh and left to dry, making certain parts of the mesh impermeable to liquids. Ink is then spread evenly over the whole surface of the screen and pushed through with a large flat squeegee onto paper or fabric below. The ink evenly coats the paper below in only the areas that are directly below the untreated, or "open," sections of the screen. Make sense?
That's the short version, and the version that was likely being used in China during the Song Dynasty (with real silk fabric might I add!).
The technique made its way to Europe in the 18th century, but was cost prohibitive for most printers because silk was so expensive. It wasn't until early 20th century that screen printing started to become a viable method of commercial printing. With the advent of synthetic fibers that could replace silk, and light-sensitive emulsion that could reproduce images photographically, the technique found huge popularity in both artistic circles, and with commercial printers and advertising professionals. Screen printing became the primary technique for mass producing posters, paper advertisements, and public service announcements. Due to the new affordability of materials, ease of process, and low space requirements, screen printing became a popular form of independent expression, underground resistance, and political activism. The screen printed aesthetic became synonymous with political commentary to the point that it is often reproduced digitally in modern design to convey a youthful tone.
Screen Printing technology has improved with time, allowing modern screen printers to take advantage of a new host of tools to create a wider variety of printed goods. Light-sensitive emulsions mean that we can reproduce photographs or drawings instead of drawing our designs directly onto the screen with glue. To accomplish the transfer of a drawing, an artist creates what is called a "film positive" which is precisely the inverse of a traditional film negative (like in a 35mm camera). Film positives are generally created by printing a black and white drawing onto a clear plastic sheet of transparent paper using either a home printer, or a specialized printer that produces very rich blacks. You then coat your screen with a light sensitive emulsion (that hardens when exposed to UV light), place your film positive on top, and expose both to UV light. This is called "exposing the screen." Most screen printers use a specialized light bed for this, but some will use the sun.
At this point the hardened emulsion will remain in the screen, and the emulsion underneath the black parts of the positive will remain soft and water soluble, allowing the printer to simple wash it away with water. All that's left is to print!
Printing could be a separate article all together. There are different types of ink, different things you can print on, and a myriad of different ways to mess up! But let's keep this simple...
You print an image by applying a thick ink to your screen, and pulling a heavy squeegee (yup, like a window squeegee) across the entire image, depositing ink on the areas where the mesh is open (yellow in the above photo). This results in an even distribution of ink, a smooth finish, and with luck, a perfect print!