There’s a dozen YT videos on this that are easier to understand than words alone. If it’s old tongue and groove oak, it may be hard to find the same width and thickness.
It'll depend on what your flooring is but you'll need to carefully remove the damaged pieces and replace them with new pieces. There are loads of videos online that will give you an idea.
What sort of flooring do you have? What is the damage?
Assuming it is hardwood strips. Cut a slit and pry up the wood. Most likely it is "tongue and groove" so each piece holds the next one down. You may need to cut part of new board's tongue or groov off to get it into the hole. Construction adhesive can fix it into place.
Sometimes you can "steal" a matching piece from a closet or other less visible spot.
Lever up the floorboards, if nailed inplace or unscrew. Measure, cut new board and replace with either nails or screws as before....