Choose tiles that are the same thickness as the existing tiles, carpet or other flooring on either side of the doorway. Each tile should be 12 inches square. This will allow you to make very simple cuts.
Install a diamond pad on the hand-held grinder. Grind the edges of each tile so they are slightly rounded and smooth. Measure and mark every 2 inches along the tile in one direction.
Cut each tile into three identical 2-inch-wide pieces with a diamond-bladed wet saw, using your pencil marks to guide you. You will need one piece for each foot of the threshold length, or three pieces for a standard 3-foot doorway threshold. Round any sharp tile edges with the grinder once the tile pieces have all been cut.
Wipe the threshold tiles with a rag to remove any sanding debris. Remove any existing molding or flooring along the threshold so the existing backer board is exposed and you have a flat surface. Dry-fit your threshold tiles to ensure they fit along the area well and are even with the flooring around them.
Mix thin-set mortar with a shovel until the consistency resembles peanut butter. Follow the directions for your particular product to add the correct amount of water, since this will vary. Wait 10 minutes, and mix the mortar again to correct any separations.
Spread the prepared mortar along the threshold, using a notched trowel held at a 45-degree angle. The mortar on the threshold should look wavy, not flat. This texture is necessary to help hold the tiles in place.
Lay one tile at each end of the threshold. The outside edge of each should butt up against its corresponding doorjamb. Tile along the rest of the threshold length, butting the end of each tile up against the end of the previous one to create a continuous threshold strip.
Allow the mortar to dry for 24 to 48 hours. Use an alternate doorway to enter and leave the room, if possible.