As Bob and John stated, you will need to join a club to get on most tracks. Joining is merely a small yearly fee of about $40. The clubs will go to different tracks in your area as well as LR. Check out clubregistration.com and motorsportreg.com to find clubs and schools that have events at the tracks in your area. Then check out their DE (Drivers Ed) program and you will be good to go.
I belong to PCA Metro NY and also run with different PCA groups, Trackmasters, Lotus Cup and Hooked on Driving. All have great DE programs that basically include instruction as long as you are in the novice, beginner and intermediate levels.
Lime Rock is a nice facility, pretty good food at the concession as far as track food goes, but not my personal favorite track for a variety of reasons; i.e. all right turns except the "Left-hander", small track, limited time due to having to interface and share the track with the Lime Rock club.
I do an event or so per year just to stay in touch but wouldn't make it my home track, even though it is the closest to my house.
Honestly I am being picky and any track is fun, even LR. I will actually be there September 7 and 8 with PCA Metro.
Go ahead and look into a club you can join and get out there, it is incredible fun.
Good luck,
Tytus