Position the tip of an iron chisel over the grout lines at the corner of the kitchen floor and pound it with a hammer to begin breaking the tile. Slide a floor scraper under broken tiles still attached to the floor to release them and remove adhesive residue. Collect the broken tile and debris with a shovel and add to a wheelbarrow.
Scrape the floor with a scrapper to remove grout and adhesive residue, so the subfloor is smooth, flat and free from any material. Sweep the floor and toss the debris in a garbage bag.
Using a chalk box, snap two diagonal lines over the kitchen floor so they intersect at the center. Use a square at the midpoint while you snap the lines, and adjust if necessary so they are level and 90 degrees off each other.
Spread thin-set mortar over the floor with a notched trowel, directly under the point where the two lines intersect. Apply enough mortar for four or five tiles.
Lay a tile into the mortar at the intersection. Tap the corners of the tile with a rubber mallet to help it set. Lay additional tiles over the mortar, putting spacers in between.
Spread a short length of scrap two-by-four-inch lumber over the tiles. Tap it gently with the mallet to set the tiles in the mortar and level their tops.
Spread thin-set mortar on the floor next to the installed tiles and continue the process of laying tiles, working your way in a grid pattern from the center to the perimeter. Continue inserting spacers between adjacent tiles as you lay them, and tapping a length of two-by-four spread along their top to ensure they are level. Cut the tiles for the perimeter of the floor with a tile cutter to ensure they fit the space. Let the tiles set overnight.
Remove the spacers when the mortar dries. Mix grout with water according to label directions. Insert the grout into the space between adjacent tiles with a grout float. Scrape excess grout over the surface of the tiles with a damp sponge. Let the grout dry for hours, or longer.
Seal the grout between the tiles to increase its resistance to stains and leaks. Depending on personal preference, spray the water-based grout sealer over the grout, or apply it using a brush or roller. Wipe away the surface of the tiles to remove sealer residue.