Apply your sealant to the travertine tile using your paintbrush. Take care to seal only the flat top surface of the tiles, not the spaces in between and not the holes in the surface. Let the sealant dry for several hours.
Mix your unsanded grout in a bucket with water, stirring it with your putty knife to the consistency of thick mud. Let it sit in the bucket for 10 minutes.
Re-stir the grout, scoop it up with your grout float and apply it over the tile. Run the float across the tile surface with the long edge of the float at a 45-degree angle, pressing the grout into the lines and into the holes while squeezing it off the tile faces.
Let the grout sit in the lines and the holes for one to two minutes. Wipe down the surface of the tiles with a damp sponge, taking up any excess grout on the flat part of the tile without removing it from the lines or the holes.
Let the grout cure for at least two days. Re-apply a second layer of sealant, this time covering both the tile and the grout.
Seal the tile with your paintbrush, keeping the sealant out of the spaces between the tiles. However, do seal the insides of the holes on the tile surface. Let the sealant dry.
Mix your unsanded grout as before. Instead of applying it over the whole tiled area with your grout float, use your putty knife to carefully apply it only to the lines between the tiles.
Smooth the grout lines with your sponge, taking care not to let the grout get into the holes on the tile surfaces. (If some grout does get into the holes, immediately clean it out with your toothbrush.)
Let the grout set for two days. Re-seal the whole area, tile, grout and all.