When I first started to make boxes I used the simplest method I could think of, the solid rock top. The top it the rock and it fits to the box with a single layer of wood glued to the underside. The top can be exactly the size of the box or overhang as in the case of this green jade-like top on redwood burl.
I start with the rock, slab and trim and pre-polish to assure I have something that will be showy and interesting. Then I think of the box. The length and with are set by the length and width of the stone, but the height is variable. Generally, I don't think it a good idea to make a box so deep that you can't get your fingers in to retrieve a precious item. Long deep boxes may have a function to hold long items, but you would have to custom design something to fit that sort of purpose. Some of the smaller boxes I have made are not very practical so have a decorative function only.
After you build a box that is slightly smaller than the slab you have, sand the edges so it is nearly the finished dimension. Place the box on your slab and then mark the edges so that you can match the rock to the box.
Trim the rock on the flat lap or grinder.
To create the inner lid, scribe a line on the interior of the box on a matching piece of wood.
Sand or plane the insert to the scribed line. Don't sand beyond the line. You may need to adjust a tiny bit at a time to give it a loose fit for the top and a tight fit for the bottom.
I generally will chamfer the edges on the lid insert so that it can be inserted into the box easily. I pre-sand the lid with 220 but will not do much sanding on the edges. I will also polish the top and edges using Tripoli.
Glue the top insert to the top rock with a polyacrylate glue. Carpenters glue will not work!
Place the box atop the lid to adjust it so it is properly fitted. Set it aside to dry.
Don't worry about pencil marks you make on the wood. A little isopropyl alcohol will remove any carbon.
Make the bottom the same way as the top only aim for a tight fit. Carefully glue the bottom to avoid squeeze-out in the box. To assist in this, only glue the bottom 2/3 of the piece so that it does not smear glue on the sides of the box as you press it into place. Tap it in flat, then sand.
After a final sand of 220 and then 400, the box is then polished with Tripoli and then waxed. A simple box with a pleasing outcome.