(for moonyinthesky, but also for anyone interested.)
The Quaker Information Center has a handy little FAQ right here that covers a lot of the basics, including a few locator services for all over the world. They also have resources for more in depth research. Once you find a meeting close to you, if you want to learn more than what they have on their website, you should try to find the Faith and Practice guide of their Yearly Meeting. The YM is just the larger regional group they belong to: for example, the Atlanta Friends Meeting is part of the Southern Appalachian Yearly Meeting and Association (SAYMA). (This locator for the Americas tends to list the YM each meeting belongs to.) The F&P is long. Don’t worry about reading the whole thing, just scan the index for things you have questions about. The Faith and Practice guide usually covers everything from the values the meeting tries to uphold to the processes they use to hold business meetings and make important decisions. Obviously, unless you’re just very curious, you won’t need to know about that unless you decide to really get involved in the nitty gritty of how a meeting runs.
I did a lot of reading around the QIC website and the AFM website when I first started learning about Quakerism, and when I decided I wanted to learn more, I turned to books. Hopefully your library has some on hand, or you can ILL them. Some Quaker meetings will have their own libraries if you’re able to visit a Meeting House. Books I have read/am reading(*) or plan to read are
Being a Quaker: A Guide for Newcomers*
The Quakers: A Very Short Introduction
An Introduction to Quakerism
Honestly, the best way to learn about Quakerism is going to be to get involved. It can be hard at first, since Meetings are silent. I think Britt and I went to three or four meetings before talking to anyone. But after a while it will get easier. Attend potlucks or classes they might offer. If someone says something in a meeting that touches you, let them know afterwards. Volunteer to help in the library or with childcare or setting up coffee before meeting or cleaning up afterwards. I think Quakerism is the most beneficial when you get involved with the community outside of just attending meetings for worship.