Building a robot usually starts with an idea about the mechanics. What is the mode of propulsion? How many motors do you need? A good way to make the robot's movement dynamic and smooth is to use springs to dampen and return limbs to a center position. The idea with this robot is a radially symmetric body with four legs. Paired leg-centering springs give the robot a bias for movement, or "forward". Each leg is at an angle, making the leg lift the body at both ends of the limb swing. Correct sequence will make the robot walk forwards, and simply reversing the phase of one legmotor, in this robot either of the frontlimbs, will make the robot turn. Reversing phase on both frontlimbs results in the robot reversing.
Once the mechanics are done, the motors need to be activated in some order to make the robot move. With BEAM style robots, this is usually achieved with a nervous net, which consist of a number of oscillators, also known as a central pattern generator. One two node oscillator, or bicore, can be used to generate the signals needed to move a single motor back and forth. The timing is set with resistors and capacitors, and additional resistors/caps connected/disconnected with, for example, a whisker-actuated limitswitch, can be used to affect the timeconstants. More nodes, neurons, can be chained to add delays or more complex behaviors. The signals from the nervous net are fed to an H-bridge or similar motor driver circuitry.
Aesthetics is an often overlooked aspect of robot building. Until self-replicating robots become a reality, the only way for robots to reproduce and evolve is through smartish apes with screwdrivers and such. Making the robot look interesting increases the chances that someone else gets inspired to make more robots!