Here's a quick run down as I understand it.
GNAS Field, mainly shoot roundels. (They do shoot animal rounds as well)
NFAS only shoot animal rounds
EFAA only shoot roundels.
All societies split you into groups which you walk around the course with.
On a GNAS roundel (FITA) course you shoot 3 arrows from one peg.
On an animal round you shoot your first arrow from the furthest (usually) peg. If you miss you go onto the next one, if you miss again you go to the last peg. You score according to the arrow that you hit with as well as where you hit.
A 1st Kill is worth 20points, 1st wound 16. 2nd kill 14, 2nd wound 10, 3rd kill 8, wound 4.
I don't know how EFAA work.
I don't loose or break too many arrows, out of a group of 4 longbowmen we can expect to be one arrow down at the end of the day. (fortunately for me it's usually someone elses!)
My advice is to find a local GNAS field club if you can and try it, since you are already a member. If you like it then look into NFAS or EFAA if you want something a bit more different.
NFAS tend to be more relaxed about their shooting than GNAS, but this can mean less safety concious as well. GNAS field archers tend to be the ones in bright colours, NFAS in camo! (This is a generalisation before anybody flames me for that coment!
)