For a full redo, you'll want to get a sander and then refinish the floors. It's a lengthy project. Here's a video from Lowe's https://www.youtube.com/watch?v=xQtjCu87zWY
I agree, sanding and refinishing them is the best way.
Yes, you’re fortunate you’ve got very old floors as the laminated wood floors cannot be sanded down.
The kind of professional upright sander needed is very big & hard to control- and if you decide it’s not for you, I’ve had two of my homes (1901 & 1948) professionally sanded, after I removed the base shoe for them.
If you think it might work, you could try deep cleaning. Here are a couple of mopping solutions that might work.
1 cup hydrogen peroxide
2 gallons hot water
1 cup apple cider vinegar
1 Tbsp blue Dawn
Mop with a damp mop which make takes several applications.
There are 2 really good products for renewing without refinishing:
S C Johnson One Step No Buff Wax is the other but I couldn't find a link for it. I've bought it at Lowe's, Home Depot, and Walmart at times.
I've used both of these to renew wood floors in houses built in the 1950 - 60's that had carpet over the hardwood for years.
If you have the determination, focus, and patience (as well as good knees and shoulders), you can sand, re-stain and seal yourself, but it will take time. The key is to tackle the smallest room first, then determine if you want to spend the money for professionals to do other rooms. If you go that route, check credentials, get written specs, written guarantee, and note how long you'll need to be without that space.
Doing it yourself, even a small room (7x9) may take a few weeks, if the older hardwood floors are in bad shape and need attention to deeper scratches larger spaces between boards, need to repair baseboards, etc. Once you see your finished work, you'll wonder why you didn't do it sooner!