Place the marble threshold on the hardwood next to the area where it will be installed to check for size. If the threshold is longer than the opening, mark the place with a pencil where it needs to be cut.
Cut the marble threshold to size on a tile wet saw. Line up the pencil mark with the blade on the saw and push it firmly into the saw blade until it is cut through. Let the marble dry thoroughly before installing.
Double check the size and placement of the threshold on the hardwood. Remove the threshold and set it aside.
Scoop up some thin-set mortar with the trowel and apply it to the area where the threshold will be installed. Rake the mortar with the trowel until grooves appear that are all of the same depth.
Set the threshold down on the mortar and beat it into place with a rubber mallet. Fill in the gaps on either side of the threshold where it meets the hardwood with a thin bead of silicone caulk. Allow the threshold to dry in place for 24 to 48 hours.