Lightly sand the round table top with fine-grit sandpaper, until the finish is no longer glossy. Clean away the dust with a vacuum cleaner and a damp cloth.
Arrange the tiles until you find a layout you like. Keep the spacing consistent by placing spacers between the tiles. Cut the tiles along the edge to size, with a tile saw. Mark a starting point for the tile with a pencil. Remove the tiles from the table.
Spread tile adhesive with a notched trowel. Press the tiles into the adhesive, and place spacers between the tiles. Allow the adhesive to dry overnight.
Remove the tile spacers from between the tiles. Spread grout over the tile joints with a rubber grout float. Remove the excess grout with a damp sponge. Let the grout dry overnight.