Tiling a room is easy -- until you run into obstacles like walls or thresholds. If you treat any object that interrupts the flow of the tile the same, you will understand how to butt the tiles up against them. Since different materials expand and contract differently either simply from movement or from temperature changes, you need to provide a joint where the difference is absorbed between the tile and the threshold.
Things You'll Need
Tripolymer rubber sealant caulk
Lay the floor tiles across the middle of the room until there is no space left for whole tiles. Start with the threshold to start cutting tiles.
Lay one tile in front of the threshold so that it butts up against it and lies over a previous tile.
Mark the tile on either side at the points where the previous tile ended. Before actually marking the tile, move the mark 3/8-inch towards the threshold to allow space for an expansion joint between the tile and the threshold. Add the measurement of the amount of space between your tiles. For instance, if you are spacing your tiles 1/4-inch apart, add 1/4-inch to the 3/8-inch to get a mark 5/8-inch away from your original mark.
Lift the tile and make a line between the two points with a straightedge and pencil. Cut the tile across the line with a tile cutter.
Set the tile in place between the rest of the tiles and the threshold using thinset as with the other tiles. Use a spacer between the tiles to continue the pattern of your floor. Continue with the next tile, until you have covered the area between the threshold and the tiles. Allow the thinset to dry overnight.
Vacuum out the space between the tile and the threshold. Fill in the 3/8-inch space with tripolymer rubber sealant caulk using a caulk gun. Smooth with a jointer tool. Seal with the rest of the floor after grouting and drying.