Try wiggling the cranks. You should be able to tell if the spindle is loose in the bottom bracket, or if the crankarm is loose on the spindle. If it's the first, you'll have to remove the non-drive crank and tighten the adjustable cup. If it's the second, give the cotter on the loose crank a few taps with a hammer (while supporting the crank with something underneath), and then snug down the nut (these strip easily, so don't go too hard on it). If nothing is loose, that suggests something is probably bent.

I'd also recommend posting this in the Classic & Vintage section. You're probably more likely to find helpful advice over there. Cottered cranks aren't that difficult to deal with. The main problem is that you are likely to destroy the cotters if you try to remove them with a hammer (you can still buy replacements, although modern cotters are generally poor quality). There was a somewhat recent post in C&V about making a cotter press from a cheap Harbor Freight chainbreaker, which is worth taking a look at. Also, if you have a local bike coop, they're likely to have appropriate tools and people used to working on these bikes.