if it's a Gardnerian coven, then you can expect a few things to happen:
1) to be given a complete BoS containing all the coven rituals, laws, charges, rites, incantations, associations, herbal remedies, and some auntie's recipe for nettle soup. when i say a complete book i mean a complete book, it will contain everything you will need to be an active member of the group. everything. you will be commanded to copy the BoS word for word.
2) you will make oaths and promises to the Coven to not reveal any of their secrets, or indeed to reveal to anyone outside of the Coven that you are in the Coven, or who any other members are.
3) you will be initiated via ritual. you will be initiated by someone who will recite his initiator, and who initiated him, and who initiated him, and so on and so forth, all the way back to Gardner himself. you will be expected to learn that exact line, as that would be the line of your own initiated tracing back to Gardner.
after that, the group will hold rituals for the Wiccan wheel of the year, help each other on an individual basis to grow and achieve within your own powers, swap literature, compare notes etc. a Gardnerian coven is a very educational one, not a social one.
Gardnerian covens are the ones i know the most about simply because a good friend of mine who i chat to a lot is an ex-Gardnerian. other than that, when i was Wiccan, i was a solitary practitioner... well, mostly anyway. i was involved in one small group, myself and two others, but we were certainly not what any of us would have called a coven... and we were mostly either down the pub drinking or in a field invoking.