There are at least 2 free drinks events a term (sponsored by law firms) and at least one ball in michaelmas and another in hillary (these are often big events: past venues include the Royal Courts of Justice, Warwick Castle and the Roman Baths in Bath- you can expect transport, champagne reception, 3 course meal with wine and dancing for around £50 for members).
Often there are few if any graduate recruitment reps available at these types of events, but there are a lot of other ways to meet them- 2nd year lawyers tend to be bombarded in michaelmas with flyers for events run by different firms and it's pretty easy for non-lawyers to find out too.
In addition, the law society puts on talks by well known figures in the law (e.g. Cherrie Booth, David Pannick) and some firms run recruitment events in conjunction with it. They also run mooting competitions and workshops and produce a magazine, for which there is usually an essay competition.
Lots of people join law soc for the social events even if they don't want to be lawyers and you can also get involved in the committee if you want to (again, whether you're a lawyer or not)- it's a good thing to have on your CV and a great way of meeting lots of graduate recruitment people.
Cost when I joined 3 years ago was less than £20 for membership for the duration of your studies and you can also join for a year, though it's only about £5 less so theres not much point unless you are a finalist or a visiting student.
Some of this info may be a little out of date as I joined 3 years ago and was abroad last year, but in general this is what it does.