I have some old books and wonder what methods exist to preserve them?
(The paper seems somewhat flimsy.)

How old are your books?

http://www.nytimes.com/1981/12/01/science/an-acid-devours-many-old-books-chemists-race-to-stop-decay.html

What makes these particular books worth saving to you?
When I was younger I tried to save a lot of older books I had.
Finally realized that most were simply not worth the cost and bother

Thanks for the input.

Some books are printed on acid paper (think newspaper) and will harden, yellow and crack with age.  Cotton linen fibre paper may not flex, but it holds up and I've several books that are over 150 years old.

Clean hands when handling.  Hot soap and washer.
If you're going to read it, support the ends of the book with sandbags.  That keeps the spine from cracking.
When not reading or using the book, store it flat in an acid free, archival quality book box. Gaps between the box and the book should be filled with acid free tissue paper.  Said box should be kept in a climate control environment that is free from bugs (don't feed the bugs).  

I havel boxes for my more rare and antiquarian books.

Oxygen free (e.g, sealed in xenon, or maybe nitrogen or carbon dioxide) container in a temperature and humidity controlled environment.  Like they have for the U.S.  Declaration of Independence and Constitution.

Best of luck.