Most so-called "siamese" puzzles are based on the idea that you take the edge pieces from a puzzle, cut them in half, and glue the "mechanism" ends together. For example: here are the pieces of a Rubik's cube.
By cutting two pieces and connecting the ends with the protruding bits, you can create a "siamese" puzzle. For example:
What you see above is a picture of a fused edge piece. It has the active mechanical part of both cubes (active mechanical part is the part that hooks under the center). Below is a fused corner piece.
The fused pieces are used as a way to attach the two puzzles while retaining most of the functionality. The most functional siamese puzzle that I have seen still lacks movement in the U,E (equator),and D layers, and thusly must be solved as a bandage cube (see Jaap's Puzzle page at http://www.geocities.com/jaapsch/puzzles/)
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