Fixing a soft water damaged floor for as cheap as possible

Hi
The floor in front of the kitchen sink in the house we are living in is soft from water damage, and we have boards over it, so we don't fall through the floor while washing the dishes.
I want to fix it before the winter, for the smallest amount of money possible (because we are kind of lacking at the moment) and am wondering how one would fix that kind of damage?
would I have to change the whole floor or could I do it locally, and most important, how do I do it?
Thanks so much