Plastic is easy to work with. Most stores selling sheet plastic (such as Taps Plastic) also optionally cut sheets into specified dimensions. With a fine-tooth bandsaw, saw table or circular saw, you can also cut sheet plastic easily. You can also score and then ``break'' sheet plastic into predetermined sizes. Drilling plastic does require a little practice because plastic (especially acrylic) is brittle.
To put pieces of a plastic chassis together, you can use glue. You can use special cement for glueing acrylic, epoxy or even hot glue. For pieces with very clean cut edges, acrylic cement works best and looks best. For unevenly cut edges, epoxy and hot glue work better because they fill in the gaps.
One strange problem with plastic chasses is that the chasses tend to be too light. Yes, people need to add extra weight just to make sure the robot does not topple (to the front)!