As I was reading the posts a few things came to mind:
Some jamming sessions will call a tune and then the tune is passed around the circle. Everyone taking a verse or chorus. Other places, like here in my home town, the person calling the song plays and sings it all the way through, everyone else plays accompaniment. This is the easy way. If you do not want to sing and play (like in the first way I mentioned) all you have to do is lean back and the song progresses to the next person.
Come with some songs you would like to call out. Yep, here you can have sheet music. Lot of the guys will have the lyrics to songs they want to sing, thus they have music stands and sheet music with them. So if you feel more comfortable with your gig book, bring it. http://www.flickr.com/photos/kansase...n/photostream/
That camp stool music stand [with one leg shorter] in the middle of the circle is an example of what is used in Mountain View, Ark.
Here is another music stand, with a light. http://www.flickr.com/photos/kansase...n/photostream/
Looks like its a wooden TV tray.
As mentioned take notes of the songs being called and work on them at home.
I bet there is a weekly circle within 35 miles of your place, find it and go join in.