Step 1: Prepare Box

Start with a box. I bought an unfinished one from a craft store but you could also build your own (see here, here,hereand here for suggestions.
Ideally, you should use a box with a recessed lid, to provide a place for the glass to sit. You can add this to a regular jewelry box by glues mosaic tiles around the edges (see here)
Select a stain and apply with a brush or rag. Once dried you can determine if you would like to add more coats to make the stain darker. Let dry for 30+ minutes and then paint on a layer of polyurethane.

Step 2: Create Sea Glass Mosaic and Seal

Since it was a small area, I laid out the glass on a card the same size of the box top.
Apply tile adhesive to the box top. I put the adhesive in a ziplock bag,cut the tip of and squirted it on the desired area. If you have flat sea glass you could also simply glue the pieces down with hot glue/craft glue/superglue, etc.
Assemble the mosaic. Clean of any tile adhesive that gets onto the top of the glass immediately. I used a ruled that I pressed over the top to get a flatter surface.
Since this pieces is not like a table that needs to stand up to a lot of wear, it is optional whether or not you decide to grout the piece (see here for instructions). I decided not to and instead applied stone sealer and a thick layer of polyurethane.
I glued a small starfish to the inside of the lid
I made these as Christmas gifts and presented them with a sea glass necklace inside.