We are a Vex team, so this might not apply (though I know many FRC teams use Vex for prototyping). We typically meet about 4-5 times through the summer for 3 - 6 hours at a stretch, and an average of 5 of our 7 members show up at a time. We try out original designs and also look for designs on the internet and try to reconstruct those. Sometimes, when we're really on top of things, they actually get documented (like
here).
Other times, we'll invite other teams from out of town to join us, as described in post 18 of the
Vex Summer Projects thread. When we do this, the mentors try to create a short list of possible projects that would be practical for the allotted time, and once everyone is together, the teams decide what they want to build and how they want to subdivide the tasks.
Summer is a really good time for everyone to get in their share of building. During build season, things are so hectic that sometimes the less experienced builders don't get as much of a chance, since we're trying to get everything done as quickly as possible.