You'll likely start with an orthopedic exam and x-rays. In my area, those can cost as little as $50 (on top of the office visit fee), or as much as a few hundred, depending on the number of views needed, and whether sedation is needed. This needs to be managed though--letting the dog suffer in pain is not an option.
Arthritis often sets in with senior dogs who've managed all their lives with imperfect-but-not terrible hips. Even on a limited budget, that's treatable--generic veterinary pain meds are very reasonably priced (e.g., 60 tablets of carprofen costs $30 or so through KVSupply.com (with your vet's RX), and that's enough for 1 to 2 months; tramadol and gabapentin are generics available at any human pharmacy for around $10 for a month's supply (again, by RX only)).
Talk to your vet about affordable pain management -- there are effective options that can fit into even very tight budgets.
If you are able to do more for the dog, laser therapy, acupuncture, and Adequan therapy are all beneficial. The Adequan injections have nearly miraculous effects for many seniors with arthritis (cost varies, but it's a month of 2 injections a week, then stepping down to every other week or once a month). There are lots of threads here about supplements that work, too.
The knuckling under, though, is worrisome. I really hope it's not DM.
I have a senior now, too. It's so hard to see them decline.
ETA: do a search for the chicken bone broth recipes here posted by both Gatorbytes and Carmspack. That's something you can make at home, using your leftover carcasses when you pull off the chicken meat for dinner, and it's supposed to be very healing for joint pain.