Dear Kathy
You can certainly try bleaching with the strongest wood bleach available. It's called Klean Strip at www.kleanstrip.com. It will turn the dark areas an off white color. You will need to do this after the floors have been sanded, but before any finish has been applied. The wood is very susceptible at that point. Don't spill anything on the good wood.
The off white colored spots will need a light colored wood stain to blend them in to the rest of the floor. It's quite an art. You will want the color to blend in with the final finished color of the floor, not the bare wood.
Or you can darkly stain the whole floor, after bleaching. The spots may show up a bit, but no so much as now. And lastly, major repairs, or replacements. Or a combination of all of these methods. Find an old (or young) floor master in your area, that does these things, and will give you advise in person.
And please read my article, which can be found at the top of this web page in the search box on hiring a contractor. If you cannot find someone with good touch up skills, have the floor sanded only and do the bleaching-staining and finishing yourself. That's the fun part anyway.