How to clean and play analog reel to reel tapes

I have come across several analog reel to reel tape which are falling apart. The oxide/binder appears to be falling deteriorating making the tapes very difficult to play. The heads on my reel to reel player tend to "gunk" up after only a few minutes of play time and require cleaning before the tape can play again. Even then I can hear a "squealing" sound from the tape that is playing. These are recordings of my family (e.g. voice of my great grandmother etc) and cannot be replaced. Some are over 40 years old. I would like to transfer them to CDs. Can someone help and guide me on how to best handle this task. Of course, the first step would be to clean and play them. Any suggestions on the least expensive route to do this. Your help will be greatly appreciated.
I have not used this method, but I've seen references to it for quite a few years. If you have a non-critical tape to test with, start there.
I've never done this personally, but I intend to try it someday. I would suggest not playing them until you're ready to archive them. Try this link on baking.
I hope this helps

If your tapes have already deteriorated to the point they are flaking, and the residue is clogging the heads on your tape deck, you may have larger problem than just cleaning them so you can archive them. Given their irreplaceable nature, I think you would be well advised to find a professional archiving service that specializes in restoring old magnetic tapes. I recently did this for a batch of old magnetic tape voice recordings of family members who are long gone, and I'm really glad I spent the money and had it done right. (I also had professional company transfer a bunch of 8mm home movies made in the 1940's onto videotape and CD-ROM, added a soundtrack, and gave them for Christmas gifts to the whole family.)

If you botch the cleaning job, the tapes may be ruined for good, so do it right the first time.
I couldn't agree more with Scott on this and strongly urge you to follow his advice. I, too, had a similar issue with some audio tape and, later, some old 8mm home movies. After partially ruining one audio tape of my grandmother singing in a wedding during the 1940's, I had all the rest done professionally. It was a bit "pricey", but ask yourself how important the tapes are to you. Next, estimate the cost you'd pay someone for these tapes if they didn't already exist. I'll wager that the price would be much higher than the restoration. Good luck. If you live in the Bay Area (CA), e-mail me and I can give you a couple of good sources for the work.