I am looking to incorporate some butterfly key joints into a dining table design I am working on, but know very little about how to construct these joints. Any information would be greatly appreciated.
WOODCRAFT and many others sell a router inlay set or kit. Some have pre-made templates available. Taunton Press publishes the series of Tage Frid books on furniture-making; the volume on shaping, veneering and finishing has full explanation and instruction on inlaying with routers.
First, cut the Dutchmen from an end grain strip. This is so that the grain on the plug runs the length of the plug, and is long grain, not end grain. Make them all at once so they are all the same size. Cut one or more strips to leave yourself plenty for the job at hand, as well as some extras, since the jig is made to the size of the patch. Cut them on a tablesaw, very carefully, being sure that the end grain strips are solid, without splits, and use a proper, full length notched pusher. About 15 degrees is what I use for structural Dutchmen, but this could vary, especially if yours are only decorative.
On a piece of 1/4" Baltic birch ply, or MDF, or something else flat and solid without voids, mark around the key, and waste the center, with a router, jig saw, or chisel. Stay right at the line, and not beyond. This is the template pattern for a template guide. Use a large enough pattern piece to easily clamp it to the stock.
Place the key on the stock to be mortised, and carefully mark around the key with a marking knife. Then set the template over the marked area, clamp, and rout the mortise to the depth desired. For structural ones, I often go to about 1" in depth. Because the router bit is of a smaller diameter than the template guide, you will have a thin strip around the hole; in other words, the hole is too small by just a bit. Finish the mortise with a paring chisel. You might be taking off only 1/32nd of an inch with the chisel, which is quite easy, as your chisel will register in the marking line recess made when you did the layout. One little trick is to take a smallish chisel, 3/8" from a flea market is fine, and file the last inch or so, so that the bevel is at a 30 degree angle to the back, and comes to a point at the back edge of the chisel, and then sharpen. This would be used for the interior corners, at the ends, so that the chisel does not ruin the sharpness of the 75 degree corners. This little, special chisel is also handy for cleaning up or adjusting the socket for a dovetail, especially a sliding dovetail.
All in all, this handmade way is probably about as quick as buying a pre-made template set, since I think it is easier to cut the mortise to the key than to cut the key (a tricky sawing operation at best) to the predetermined mortise.