Funny this comes up--several of us were talking about this yesterday. The best thing to do is just go to a shoot and bring what you have and just shoot for fun and to get the feel of it as far as scoring and how it works. Most shoots do not draw for groups, you show up and shoot with your friends you come with, or you get put in a group of people ready to go, or sometimes a single shooter will be placed in your group.
As far as what to expect, it is much more relaxed and non-pretentious than most new shooters believe. Basically, it is just a bunch of people shooting at targets and having a good time as a group--the main difference between shooting in your backyard and the local tournaments is the number of targets and the number of people. We have 10%-15% of the shooters that come to our shoots and never shoot for competition--they just shoot the fun classes, which is what I recommend to every new shooter until they get the feel of it. Most all of us started out this way and just got addicted to it and became fully immersed in it, but at our core we are still bowhunters!
The main reason most of us have bows that are dedicated competition bows is because most hunting setups will exceed the rules set in the competition classes and it is a pain, and sometimes impossible, switching bows back and forth between hunting and competition setups. Another reason for having two different bows is the two disciplines are completely different--one you just need to be accurate enough hit a pie-plate and the other you're trying to hit something that is the size of a baseball and a quarter at 30+ yards.
If you you are in Mid-TN, you are lucky because there are so many shoots. You can easily hit two different shoots on the same day every weekend, except for on ASA weekends. East TN has quite a few clubs as well, but I'm not very familiar with all of them. In West TN, 3D is not very popular and clubs are comparably sparse compared to Mid and East TN. Here is a website that will help you find shoots near you.
www.3dshoots.com
If you have any further questions feel free to ask and don't be surprised if you find yourself addicted once you do it a few times.