Adding a filler piece to the door bottom
It's easy enough to glue and screw a piece of wood to the door bottom, but it'll look bad unless you paint your door. For a nice-looking job, choose wood of the same species with a grain and color that closely match the door. A first-rate job requires a table saw and some woodworking skill and patience, but the results will be worth the effort.
Because the floor may not be level, swing the door to find the highest spot in the floor. Make a light pencil mark on the door 2 in. up from the floor at the high spot. The filler piece will be 1-1/2 in. tall and you'll want at least 1/2-in. clearance under the door.
Remove the door by pulling out the hinge pins and lay it on a pair of padded sawhorses. Carefully cut off the door at the pencil mark to get a clean, square edge.
For the most seamless appearance, construct the filler from three separate pieces, matching the width, thickness and grain direction of the door's two stiles and rail (see photo). Glue the three pieces together using biscuits, dowels or splines.
Accuracy is essential. Make sure the finished filler piece is exactly the same thickness and width as the door. Then finish-sand it to 120 grit and stain and varnish it to match the door. The closer you can match the stain, the more seamless the fix will look.
Drill four clearance holes all the way through the filler piece. Apply wood glue to the door, align the filler and clamp it in place. Then drill pilot holes in the door through the clearance holes. Drive the screws tight, countersinking their heads, and wipe off excess glue with a damp rag.