Okay Carson, here's what we did so far. I'm assuming you are using a stock Egg table, made out of cedar wood, which is resistant to bugs but also soft so be careful not to dent it while doing this work. Being in Florida, you don't have to worry as much as we do about cold temps (wood and tile contract/expand at different rates).
The first time we used 4" tiles and that does better for food prep and stuff but the winter temps make the grout crack and buckle. It was also harder to nip the tiles to make a round opening for the egg, total pain in the ass.
This time we went with those 12" x 12" sheets of 1" tiles. After day 1 I can tell you, much easier. The only special tile tools needed are a tile nipper (plier like thing), notched trowel, and a float.
First, the ends of our table are rounded, pain in the ass to tile that. So I squared them off with a circular saw. That makes your ends easier to tile and trim with wood.
we dry fit the tile pieces. We started at the front mid-line of the Egg-hole and worked from there.
Keep in mind that the top of the table edges are beveled, line your tiles up about 1/4" from the actual edge, not the rounded top. Any tiles that are going to have to be "nipped" or cut to fit, are removed. I only tried to get all whole tiles lined up.
Then we took them off and place them in about the same arrangement on the ground to keep them in order. Next tack a piece of metal flashing on the inside of the Egghole. Our first Egg table is rough around the Egg-hole because we had nothing to grout up against when we got to the hole. (God this sounds dirty). This flashing will make it even (in theory, we'll see how it works).
Now put down the thinset with the notched trowel.
Place all the whole or partial sheets back in. Now take your scrap tiles and use the tile nippers to start breaking them into the half pieces that you need. You don't have to be perfect since the grout will go right up to the flashing edge.
We are putting a tile facade on the front piece too. Most of these sheets are 4" x 12". The front board is only 3" wide, so you have to build it up by nailing a few furrow strips at the bottom to make it 4". Then put on the thinset with the trowel, nail your trim frame (I used 1" lattice trim) around the board, and insert the pieces. Our board was 37.5 inches so to get the pieces even, I had to use a few of the table top tiles as an "accent". Your table will be different but you may have to do something similar.
To make sure they hold while curing, clamp a board on them but not too tight. Then I attached trim around the table top. This is what will hold your grout in around the edges. I used 1.5" lattice trim and cut a 45 degree mitre cut on the corners. You can hand nail it on or use a brad nailer. You want the top of the trim to be just about even with the top of the tiles.
And that's where we are at tonight.
Tomorrow night we are going to grout and stain. Sheet.