I just finished fixing one and have to run out for another job. In the meantime, read this and come back with any questions.

The technique is only slightly different for stick-chairs.

Two guiding principles:
- You can't glue glue. Clean all the joints thoroughly.
- You can't glue air. Don't rely on filling gaps with glue. The exception to this is epoxy, but then that creates a non-reversible repair, should you ever need to do it again.

And...
There is a special place in Hell for people that put nails in chair joints. It is right between the room for people that put screws in nail joints and people that put staples in chair joints. Any of these rarely do good, and most often do harm. I have never seen a broken chair joint that did not split right between the hole made by such fasteners. It also creates a lot of damage trying to get these things out.

Here is a link that might be useful: regluing dowel chairs.

Thanks for the link, there is lots of good information in that article. I know that old glue must be removed and that a good fit is essential to a strong glue joint. What's the best way to fill a loose joint?

Any thoughts on replacing the screws that hold the back legs to the seat? I was thinking of something like a Miller dowel.