"How do you go about determining what kind of supports, if any, a part will need? Is it calcuation? Good CAD? Lucky guessing?"
All three to some extent, plus some experience. If you were trying to design "on the edge" and make it as light as possible and no stronger than absolutely necessary you would need to do a lot of calculations and design iterations, but this takes too long for a 6 week build.
We use Inventor to concept and design the robots, starting with block shapes. Once the generic shapes are the right dimensions, we go back and visualize where and how many bulkheads will be necessary. This relies on experience, but the CAD drawings make it much easier to visualize the stresses on the parts. The nice thing about monocoque is that it IS quick to build, so you can easily try something to see if it works. If it doesn't, you're not out much time or material.
Of course, in a rushed build with a design that was hashed out in a couple weeks, there are usually a few, "Whew, I'm glad that worked!" moments at the end.
Mike