Basically, an inlay is a puzzle that the artist cuts all the pieces for, then routs (or grinds, chisels or gnaws) out a corresponding hole in the host material (usually wood, but possibly stone, metal, plastic, etc.), and glues in flush with the surface. After filling any residual pits and sanding smooth, the inlay might have some final details engraved on it, and the lines inked.
Some people tend to confuse inlay with marquetry, which is a similar decorative technique that normally employs wood veneers, and is glued over the surface of the host object. Both methods are difficult to master, have their own specialized tools and jargon, and occupy specific niches in the decorative arts. Another craft similar to shell inlay is stone mosaic, again using its own unique equipment.
The inlay artist must start with a clear design, all perimeter lines drawn in as thin as possible (For more detailed information on this section, see The Art Of Inlay). Once the drawing is finished, many copies are made on a photocopier and sections are cut from these, each containing a complete perimeter line for each piece in the inlay. Those individual fragments are then glued to the surfaces of materials that will actually become the inlay.
A jeweller's handsaw is then employed to cut the shapes of each scrap, which are then glued together to recreate the original design. Next everything is tack-glued on the host material and the perimeter scribed around with a razor knife. When the pieces are peeled off, the resulting line is filled with chalk dust so the artist can better see where the edges to rout to are, and using a small router with a depth-guide and dental burrs, removes the area where the inlay will fit.
Upon making certain that the inlay fits tightly in the cavity, it is glued in, and when dry, sanded smooth and polished. After engraving small details and perhaps spraying a finish over everything, the inlay is ready for it's new owner.
Here are some other links to websites that show the results of inlay, marquetry, & stone inlay.