One of the great strengths of the Meetings is the vast range of talks. However, not all of these are equally accessible. An infamous anecdote from an International Congress of Mathematicians says that one lecture which was billed as being "an introduction to algebra" began with the sentence "We will assume that every topos in this lecture is Grothendieck". It should be noted that the "accessible" talks are marked by their authors as accessible; different people have different ideas of what this means!
The invited lectures are often especially accessible; the speakers try very hard to make their talks open to a very wide audience. These provide an interesting overview of modern mathematics.
Poster sessions are often very accessible; the YMN have their own poster session, for instance, and there are other sessions run by the MAA, the NSF, and other bodies. If you have results of your own, then presenting at a poster session can be a gentle introduction to presenting mathematical work.
There are some events specifically for students; the Program of events often has a section giving a list of these events. The relevant section of the 2007 Program was "MAA Sessions for Students".
The YMN runs events catering for students, such as "Undergraduate Career Paths in Mathematics", and the Town Meeting, which provides a forum for the concerns of young mathematicians.
The Joint Meetings can be an interesting experience for everyone, with a bit of preparation. We hope that you enjoyed it and that it was worthwhile for you.