Stretch your chalk snap-line from one corner of the room to the diagonal corner, with the help of an assistant. Pull the string tight, pull up on it, and snap it against the floor.
Stretch the snap-line between the two remaining corners, so it intersects the first line in the middle. Lay a square at the center and adjust the position of the string so it's exactly 90 degrees off the first line. Snap the second line to leave an X over the whole floor with the intersection in the center.
Use your notched tiling trowel to spread thinset mortar over a few square feet at the middle of the floor at the intersection of the X. Start within one section of the X.
Set the first tile into the thinset mortar between the lines. Set the second one next to it, along one of the lines, putting two spacers between them.
Set additional tiles in place, side-by-side, building out from the center toward the perimeter. Spread more thinset mortar as you go, and keep the whole pattern straight using the lines.
Measure and cut the tiles for the perimeter of the floor on your tile cutter. The cut tiles will be triangular with two factory edges and one cut edge. Lay them with the cut edges facing the wall.
Let the mortar set overnight. Remove the spacers.
Spread grout onto the floor with your grout float. Press it into the spaces between the tiles. Wipe off the excess grout with a damp sponge.