As friend Azizi said, "folk music" means different things to different people, and we have gotten into long (friendly) discussions here on just what it is, without ever reaching any conclusions.

There are many good suggestions above. I'd also suggest getting a copy of the (much maligned) Rise Up Singing (aka The Blue Book) and/or a copy of The Folksingers Wordbook. Also, depending on where you (physically) are, there are many groups that get together for recreational singing.   A (probably partial) list of these Song Circles is here.