Now that a descriptive overview of the ins and outs of running a robot has been dispensed, it is time to get down and dirty with the technicalities, starting with issues pertaining to the physical assembly of the robot arm.
The LynxMotion website has lots of useful background information to the build process (including tips about handling the Lexan plastic), and contains frank information about the limitations of the robot arms. There are also the official instructions there (the best place for them since updates can always be supplied without grief to anyone who might otherwise have been stuck with paper copies). These instructions are very clear, and provide the definitive information you need to construct the robot arm.
We make no attempt to reproduce the details of this process here, except in some exceptional instances where things aren’t quite as straightforward as the instructions make out (or at least they might be if one were to actually follow the instructions; many of the notes here correspond to situations where, to our dismay, deviating from said instructions causes some unnecessary problems—but this is all part of the joy of learning a new hobby!)