Most floors use a tongue-and-groove design for connecting adjacent strips. This design makes replacing a single strip or plank challenging, but not impossible. First, look for any nails in the damaged board and drive them as far through the board as possible by using a hammer and nail set. Carpenters use nail sets to drive nails flush with trim without damaging the trim with a hammer. After you’ve cleared the nails, it’s time to remove the damaged board and install a new one. Follow these steps:
Judy – I’m sorry to hear this. I am surprised, but it does happen once in a while. I would probably get a 2nd opinion just to make sure. If they were solid hardwood and are now too thin, then it sounds like they’ve been refinished many times. Generally solid hardwood flooring is 3/4″ thick and that is what you should get if you put in anything new. That will then last a long time and you won’t have this issue in the future.
Cut a new length of flooring to fit snugly into the space of the old board. It doesn't matter what kind of saw you use to repair your hardwood floors; just make sure the cuts are perfectly square. After trimming the board to length, turn it upside down and use a chisel to chop off the lower lip of the grooved edge (photo 5). That allows it to fit over the protruding tongue of the adjacent floorboard. Test-fit the new piece. If it's slightly lower than the surrounding floorboards, shim it up with strips of kraft paper. Then remove the board and spread carpenter's glue on the tongues and grooves of the new and old pieces. Slip the new board into place (photo 6), protect it with a scrap-wood block and tap it down with a hammer. Cover the board with wax paper, then hold it down overnight with heavy books or weights. An alternative to gluing: Simply face-nail the board with 6d finishing nails. Bore pilot holes at a slight angle, then drive in the nails. Tap them below the surface with a nailset (photo 7) and fill the holes with wood putty. Lightly sand the entire board smooth, but be careful not to remove too much finish from surrounding boards. After finding a matching stain color by experimenting on scraps of flooring, stain the boards to match the original floor. Let dry overnight, then apply two coats of clear polyurethane varnish. If the old floor is unstained, just apply the polyurethane. Denver Hardwood Floor Install
The amount you pay for installation depends on a variety of factors, including where you live and the intricacy of your project. For example, furniture removal and replacement, repairing the subfloor and removing and disposing of the old floor all bump up the overall cost of the project more than simply having an installer come in and lay the flooring does. To illustrate, some installers charge 20 cents per square foot for ripping up and removing carpeting or moving furniture. Others may charge a per-appliance fee for moving appliances.

Price is the first obvious variable to consider. It is almost always cheaper to refinish your floor than to replace it. When replacing, you must consider the cost of the new wood as well as the installation. You can offset much of this cost by installing the floor yourself, but this is a very invasive process that requires specialized knowledge and precision. You can typically refinish a wood floor yourself, with just a few inexpensive solutions. Denver Hardwood Floor Install

In general, it will almost ALWAYS be less expensive to refinish your hardwood floors. If you replace them, you need to pay for additional wood as well as ripping up and hauling away existing hardwood. If portions of your hardwood are damaged (e.g. pet stains or minor water stains), you can replace these sections and when you refinish them and it will all look new. Even if you have this, it will still be less expensive then replacing the whole floor.
Eliminate any problem spots to make the subfloor level. Sand minor humps down with a hand-held or orbital sander to make the subfloor level. To fill any dips or low spots, use a leveling compound (also known as floor patch). Mix up the compound according to package directions, fill in the dips, then pull your straight piece of lumber back and forth over the spot to flatten and level it with the rest of the subfloor.[7] Hardwood Floor