Our club (Wessex) deals with new prospective members in two ways. Firstly there are the ones that turn up in small numbers throughout the year and then there are the organised events.
The casual arrivals are either already known to us from our relationship with some of the universities or they contact us through our website. The known people just find their "niche" in the club. They tend to be competent cavers and are just moving from a higher education club to a mainstream club, they already know and have relationships with other club members and tend to just fit in. Those that contact us about caving are generally advised to come along on a couple of trips to see if its for them. They will be put in touch with somebody who will "take them under their wing" and also sort out stuff like gear for them to borrow. After a few trips they will normally apply for membership and hopefully will have built relationships with several of the members (caving together is very good for this) They are encouraged to acquire their own equipment, and also encouraged to go on their own trips or cave within a wider circle of people on club trips and such like.
We also run Formal "Try Caving" events. These tend to be for the whole weekend. Newcomers are encouraged to come along and we would also organise accommodation, food and other social events around the weekend. Lots of members are encouraged to come along and help with the weekend and with the caving.
Both ways seem to be reasonably successful