How can I repair water damage on this window sill?

Sand and restain it. Simple task. Minwax has tiny cans of stain. Once you sand off the stain marks, use a rag and LIGHTLY dip the rag into the stain with just a tiny bit of stain on it and rub into the wood. Really easy task. Don't wet the rag or you will get too much on it and the wood will suck it up too fast. Just a but and rub it out to the color you want. Top off with a coat or two of polyurethane you brush on. No nee to wait. It is indoors and you should be fine.

Clean as best you can to remove mold and water stain maybe bleach or vinegar, then sand and restain. Good luck!

Yes. Sand, re-stain and poly- if you’re worried about fumes, then use water-based versions of these items.

If the sanding isn’t addressing this, then you can hand-stain the light areas with two coats.

Dittos to Em. I don't follow the Minwax directions. I save old socks and use them inside out for staining. From your pic it looks like 'Pecan' colored stain (that's from memory, don't hold me to it). Once it's sanded, dip a sock or rag lightly into the stain and then rub in until you get the color you want. Dries quickly and can then be clear coated.

Everyone's got the same idea - but remember to protect yourself and pets you might have - from any fumes in the products you choose. To do that, you might have to wait until warm weather so that you can either remove the sill or keep that window open. I would definitely use polyurethane to top off the new stain finish. It will help prevent any further water issues on your sill (you may want to do this everywhere as a precaution!). You can find it brush on or spray on. Both work fine for me.

I agree with everyone. Sand down to raw wood. Stain and three coats of a water based poly.

Sand it down to the raw wood, stain, and then poly to seal it.

Use Cotton Buds dipped in bleach to try to remove black stains. Maybe W/up liquid and bleach mix? Then in the spring rub down and stain the entire shelf. Re-stain and seal.

scrap the area

remove rotten stuff

sand

apply wood epoxy

sand

prime and paint

Hello again. After bleach has done it's work, or before he returns home, wash down with a scented disinfectant. You could repeat this process until it is acceptable to you or the old man. best wishes.