This instructable details the robot that I built for class at school. (For the robot contest I'll tell you that I'm between 13 and 18)
Materials:
- 1 PICAXE programming board
- 2' of 7/64" metal dowel
- 1 1'x1' black plastic sheet
- 2 servo motors
- 1 9V battery
- hot glue
- 2 wheels (I used these wheels from Polulu)

Obviously, you can substitute most of these: plastic can easily be substituted for cardboard and the servos could be DC motors as well (although the robot wouldn't turn) -- etc.

A 3D CAD rendering of the pictured robot is available here!

Note: although the pictured robot includes gears, they are a little beyond the scope of this discussion and therefore are excluded from the guide.
Let's get started!

Step 1: Preparation

Cut dowels to length of robot (my chassis is 4" wide).

Cut two plastic sections: one 6"x3" and one 4" by 3". bend the 6" piece so that it's one 2"x3" and one 4"x3" piece (still stuck together).

Glue servo motors to the underside of the angle on the bent piece.

Step 2: It Comes Together...

Glue the end of the flat sheet of plastic to the end of the bent plastic.

Cut two more 4"x2" plastic sheets and glue one to each side.

Tape across the bottom inch of the hole (this way, the board won't slide out when you place it inside!).

Step 3: Vroom...

Time to add the wheels! Obviously, this is going to vary depending on your motor. Basically, glue the middle to whatever spins (for my robot, my wheels screwed into the motor)

While you're at it, tape your PICAXE board to the top of the bot. Stick the 9V in the "cargo" area (with the motors).

Step 4: Programming!

Now you're done with construction! Just plug your servos and 9V into the board (see the blinky light?) and connect the board to computer. If you don't know how to write code, here's some prewritten for you:

main:
servo 6, 75
servo 7, 225
pause 5000 'go forward for 5 seconds
servo 6, 225
pause 500 'turn around
goto main

NOTE: If this makes your robot go backwards, switch wherever it says 225 to 75 (and vice versa).

Step 5: Finishing

Hooray! You've built an awesome robot. Make the finishing touches and take it for a spin! Give it a name! Paint it. Make it "see" its surroundings! Add attachments! The possibilities are infinite. Congratulations! I hope you enjoyed this tutorial.