How should you build first Lego league robots?

Since I assume you mean FIRST LEGO League and you mean it for this year's, you build it like any other robot, it just has to be able (assuming you want to have a chance of winning) to do all of the tasks in The Game. You would have to be able to move all of the balls, the polar bear and everything else. You shouldn't spend more than a week with the building, though, programming and the project are also important and involve a lot more time. However, depending on whether you're using a NXT or RCX, there are some restrictions:

NXT NXT controller (1)

motors (3)

touch sensors (2)

light sensors (2)

lamp (1)

rotation sensors (3) minus the number of NXT

motors present

ultrasonic sensor (1) RCX

RCX controller (1)

motors (3)

touch sensors (2)

light sensors (2)

lamp (1)

rotation sensors (3)

3rd touch OR light sensor (1)