(I offer my knowledge gained from 1.5 years working in WA's biggest used book store)
Well for starters, we can rule out junk in a whole lot of ways. If it's not a first edition, it's not worth much more than any other newer book, and it's worth that to a much smaller niche of buyers.
If it's not in great shape, it might not be worth much even if it was a first edition of a popular book. Things to look at are the dust jacket (if it has one - books that old generally don't, even if they were printed with them) is it ripped/creased or stained with anything? Same with the cover - look at the edges if it's a hardcover, they can get dinged up over the decades.
If the outside looks fine, check inside. Does the binding look intact? The most notable issue is dried out glue. You'll hear the book crack as you open it if this is an issue. The cover can also become loosened from the pages without actually breaking. Also check the inside edge of the cover where it meets the spine of the book - the pages often start to tear out at that spot. Finally, check the pages themselves. Are any of them falling out? Are they dog-eared or creased? Has someone written in the book or hi-lighted anything?
If none of that is an issue, you've probably got a book that's at least worth a few bucks. The only trouble then will be finding someone who either collects or buys-to-sell old books.
If you want to figure out what exactly you have, an easy way is to search on Amazon.com for the book. Type in the publisher, author's last name, type of binding (hardcover/paperback), and the title. You should get a fairly short list of books, hopefully with your exact copy in it.
Also, could you post pictures of them? I personally collect old books (but I'm broke, so I won't offer to buy them. Sorry

)