On a subfloor of cement backer board screwed in place, dry-fit the first tiles on the floor before getting started. Position the first tile in a corner of the room where the walls make a 90-degree angle. Lay the first tile so that one of its flat sides is toward the corner and the tile's corners are almost touching the walls. Use a speed square and measuring tape to make sure the tile is centered and sitting at a 45-degree angle to the walls. Mark the floor along the top and bottom edges of the tile for later reference. From that first tile, lay out the design across the rest of the floor and mark the floor with parallel lines so that tiles can be accurately placed.
Use a wet saw to cut the partial triangular tiles that fit against the wall. Dry fit each cut tile and use spacers between the tiles.
Use a drill with mixer bit to mix thinset tile adhesive according to the manufacturer's instructions. The adhesive should be about the same consistency as toothpaste.
Spread the thinset on the floor using a 1/4" x 1/4" square-notched trowel over an area of two to three tiles up to the marked lines on the floor (Image 1). Don't cover the lines or it will be difficult to keep the tiles lined up properly. Also, don't allow the thinset to begin to dry before applying the tiles. Thinset should be sticky to the touch (Image 2). If not, it is too dry and a new batch should be mixed.
Set the first whole tile along the marks by slightly twisting it in place and pushing down hard on the tile. Fill in the corner tiles next. Use tile spacers to ensure even grout lines. After setting two or three tiles place a straight board that spans the tiles on top and gently tap it with a mallet to ensure the faces of tiles are all at the same height. Continue setting tiles, making sure to correctly place the tiles along the marks. Remove any thinset that oozes up between tiles.
Allow the thinset to cure beneath the tiles according to the manufacturer's instructions. Do not walk on the tile until the thinset is cured. After the thinset has completely set, remove the tile spacers. Clean up any debris.
Mix the grout in small batches that can be applied in 20 minutes or so. Using a grout float, spread the grout over the tiles and holding the float at an angle force the grout into the grout lines. Use the float to clean most of the grout from the face of the tiles.
As the grout on top of the tile dries and turns powdery, it can be sponged away. Use clean water in a bucket and a sponge to clean the tiles. Replace the water frequently to keep it clean for rinsing the sponge. Being careful not to disturb grouted areas. Use towels to buff away any grout film after sponging. The grout in the grout lines may not be dry at this point so be careful not to disturb it.
Follow the recommended steps provided by the grout manufacturer to cure the grout. Some types of grout require that you dampen the grout over the course of several days so that it cures slowly.