I did a similar table last year. Hadda old piece of Chestnut burl that I wanted to inlay (table top is maple and cherry). I sliced the burl, traced the pattern on top, then routed it (very carefully)...as Dan & Stick mentioned, then used 2 part epoxy, filled in the gaps. Flattened it all down (as the burl was rather proud to table top...as I intended) with a power-planer, then subsequent grades of sandpaper...etc.
Once I conquered that, I got some polished river stone and did the same thing. I laid out the stones where i wanted them, traced the outline, then using a trim-router and a 1/2" core box bit, roughed out the hole (with rounded bottom & sides) to allow me to fit the stones into the top...again, about 1/2 depth of the stone proud. Used the epoxy again, although this time, carefully added it around the edge of the stone to just bring it level to the surface of table, since I could not sand or file the cured epoxy around the stone. All of this had to be done AFTER having done surface prep to the table top (sand, prep, & at least 1 coat of poly), since you don't want to poly over the stones.
Fun project...some people look at the table and say "gee...WHY did you do that?" Others say" GEE...HOW did you do that?" Pictures are attached...