The most basic kind of tenon is a four-sided peg carved into the end of a four-sided board. The tenon slips into a similarly sized hole, called a mortise. Tenons and mortises create strong, concealed joints for fine woodworking projects, such as cabinetry or furniture. More-complex tenons include dual and triple tenons, which consist of two and three pegs at the end of the board. In addition, carpenters make angled or "mitered" tenons to join adjacent pieces of wood, such as the corners of a picture frame. Keep in mind the type of tenons that you want to make when choosing your jig.
Table-saw tenoning jigs usually consist of a framework that mounts over the table saw's rip fence. The jig uses the rip fence as a guide -- it slides back and forth across the fence while holding the work material in an upright position. You can create a table-saw tenoning jig from relatively inexpensive materials, such as plywood. However, since the jig must repeatedly slide across the table without snagging, many woodworkers use a melamine-coated particle board. Table-saw blades protrude relatively far above their tables, so table-saw tenon jigs are typically capable of cutting large tenons. Also, table-saw blades tilt, allowing you to use the same jig for cutting both straight and mitered tenons. Alternatively, some homemade table-saw tenon jigs are frames that mount into a table saw's miter slot and slide back and forth without assistance from the rip fence.
Most router-table jigs are sled-like frames that slide through the router-table miter gauge channel. These jigs often consist of a broad, thin piece of flat stock, either solid or plywood, with a thin strip mounted to the bottom. The thin strip fits precisely in the miter channel. A thicker piece of lumber on top of the sled serves as a mounting surface for the work material. Carpenters attach the work material to the mounting surface with clamps and push the material through the router blade. In general, it's more difficult to cut mitered, dual and triple tenons with this type of jig than it is with a table-saw jig.
For hand-held routers, such as plunge routers, you can build a jig that sits above the work material. A simple hand-held router jig consists of a piece of solid lumber or plywood with a square hole cut out of its center. The lumber or plywood mounts to a frame, which elevates it above the end of the work material. The hole in the jig is sized so that when you run the router around its perimeter, the router bit cuts a precisely sized tenon in the upright work material.