How do I refinish dining room chairs?

Your biggest challenge will be the fabric. You don't want to get stain on it. I would probably just lightly sand the damaged areas and dab on some dark stain to match. They also sell furniture repair pens that can touch up scratches and exposed wood to blend in. Check stain section of store to find these coloring pens. They look like a Sharpie marker. You can also use a Sharpie if you can find a close match.

This article will give you several ideas for minimal scratches: https://www.wikihow.com/Touch-Up-Scratches-on-Furniture and here is an article to repair dents (small or larger): https://www.wikihow.com/Remove-a-Dent-from-Wood

I'm not sure how many scratches/dents there are, but sanding it and starting over may be a quicker option if there is a lot of them.

Pam: Or, you can paint over the scratches and dents as part of a shabby-chic look!

https://www.anniesloan.com/techniques/how-to-create-a-two-colour-distress-using-chalk-paint

If the scratches aren't bad the easiest way is to know the exact color of the wood and type of wood. Then go to home depot or some store like that and show an older associate that color and wood type and he can help you locate the right kind of wood stain you need. Then you pour a little in a cloth and buff them out. If their deep scratches then you'll have to use a wood filler, sand it down with a 2 stages of fine grit like 120 first then 220 last and then stain it. I say older associate because no 19 year is going to know what hell their talking about. Find a old person. I usually look a person in their 50's with the beard and tape measure.

Thanks for all of the help . So far we have tried the pens but it doesn’t seem to match and the stains don’t seem to penetrate properly. We are also going to reupholster them when we figure out the best way to repair the wooden sections.

Try Gel Stain. Its thicker. I use it to grain paint aka faux wood grain over existing paint. Zar and Minwax both make nice ones.

https://www.diynetwork.com/made-and-remade/learn-it/use-gel-stain-to-spruce-up-cabinets-lamp-bases-and-more

Gel stain sits on the surface. It doesn't sink in like regular stain.