A stencil method of printmaking in which an image is imposed on a screen of silk or other fine mesh, with blank areas coated with an impermeable substance, usually a varnish-like substance, and ink is forced through the mesh onto the printing surface. Also called silkscreen process and screen-printing. A print with a varied range of colors requires screens for each color. Some serigraphs are done with a limited range of colors for this reason (http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&item=280167439573). Some, such as this, http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&item=280206585358, have a wide range of colors.
The serigraph may be an open edition or a limited edition. If it is limited, it will be numbered with the print number / edition size. If it is a "proof' edition, it will state A/P or E/A. It may be signed "in the plate" with or without a pencil signature in the margin.
All this information is essential to know, but....suppose you find a print, signed and numbered in pencil. How do you tell if it is a serigraph? The tool you need is a high-power loupe or magnifying glass, at least 10x. Look at the print under the loupe, especially where colors abutt. Since the ink is forced through screens, you should see minute overlapping of colors. This might not show up in every area, so scan the print with the loupe. Notice if the color 'sits' on the paper. There should be no dot/matrix pattern to the surface (which would indicate a modern offset litho). Colors should be smooth and continuous.