Laying floor tiles through the middle of the floor is a simple matter of arranging them in a grid that you start in the middle and build out toward the walls. Tiles that sit straight against the walls can be cut straight across with a tile cutter while tiles at the inside corners of the room are simply cut twice. Tiling around an outside corner (such as the edge of a doorway) is more complicated because you have to cut a notch into the tile.
Install your full tiles throughout the room, setting them in thinset mortar. Cut the tiles that will go straight against the walls and the edges of the floor using your score-and-snap tile cutter and install those as well. Install inside corners by making two cuts (one in each perpendicular direction) and set them in place. Leave empty spaces around outer corners. Let the tiles set overnight.
Set a full tile along one side of the outside corner, evenly spaced with the surrounding tile. Use your pencil to mark the edge of the tile where it lines up with the corner.
Move the tile to the other side of the corner and repeat the process, marking the edge of the tile where it lines up with the corner. You should be left with two pencil marks on two perpendicular sides of the tile.
Set your square on the tiles, with the two sides of the square lined up with the two marks. The corner of the square should be sitting right on the surface of the tile. Trace around the square.
Use your carbide rod saw to cut along either of the two lines, sawing at the edge and working your way inward. Stop cutting when you get to the marked corner where the two lines meet.
Put the tile on a score-and-snap tile cutter, positioning the second line under the blade. Score the blade along the line, starting at the termination point of the previous cut (the line you made with the rod saw). Snap the tile. The final piece should look like a square tile with a small square taken out of it from two edges.
Spread thinset mortar on the back of the tile with a notched trowel. Press the tile in place around the corner, spacing it with the other tiles. Let it set overnight.
Grout the whole floor with a grout float, pressing the grout into the spaces between the tiles. Wipe the excess grout with a damp sponge. Let it set up for two days before using the floor.
Wear eye protection when cutting tiles.