Hardwood floors are usually interconnected when they are laid down. So, if you have a damaged section of your flooring, you can't just pry it up. You would have to take out the whole floor first! This guide will give you some advice on patching a section of your hardwood floor.
First
If you kept the extra wood from when the floors were laid down, you should use those pieces, since they will match what you have. Otherwise, go to your local home improvement warehouse and find out if they have the same brand and model of flooring. If not, you can sand and refinish other flooring of the same wood type, but it won't blend as well with the wood surrounding it.
How to Patch Hardwood
First, determine the area needing to be removed for this patch to be successful. Keep aesthetics in mind as you do this too; you may want to remove a little more wood than is necessary in order to preserve the "staggered" look of a hardwood floor. You can use a circular saw to split the planks in two. Cut down no more than 3/4 inches into the wood, not too far, so as not to damage the subfloor.
Score the ends of the damaged planks with a utility knife and a straight edge. Make sure the line you are making is square with the wood. Use a hammer and chisel to cut along the scoring, angling inward to prevent damage to the other planks.
If necessary, take the wood off in layers with the chisel until you reach the subfloor. Once you have all the necessary pieces removed, you can get to work on the patch. Cut the patch to match the length of the area that is missing and, using a table saw, cut off the bottom section of the groove (not tongue) side. This will allow you to drop the piece in the hole you've made.Face nail with a nail gun or a hammer and nail setter. If the replacement pieces are unfinished or finished differently than the surrounding floor, try to approximate the same color through a combination of stains (sand the piece first if it is already finished). Once the staining or refinishing is done and you are satisfied, use some wood putty of a matching color to fill the holes from the set nails.
Some hardwood damage may be so extensive that you need to buff and re-finish the entire floor. Should this be the case, you may want to hire professionals who know how to operate that kind of equipment, as you could seriously damage the wood in the process of trying to strip the finish off. There's no shame in hiring the pros; they don't have years of experience for nothing!