Protect your books from prying hands. Human use is the biggest threat to keeping antique books in good condition. Specifically, when the books must be handled, the cover and binding should be supported as much as possible. These areas are under a lot of pressure when the book is opened.
Control heat. The environment of these books should be around room temperature and relatively static.
Control humidity. Some recommend using a dehumidifier to make sure the books aren't in a humid environment. However, too much dryness is also bad. The more control over humidity, the better.
Keep your antique books in the dark. Despite sounding kind of sinister, this is a necessary step to maintain your books, as light dries out the books and causes print to fade.
Repair bindings only under expert supervision. It may be tempting to glue pages and bindings back together, but usually, a novice will end up spoiling more than he/she fixes. Book binding experts will know how to fix the pages of your antique books to the cover and binding the right way.