How does one get a job as a LEGO designer?
There's a nice interview with LEGO Designer Mark Stafford on The Brothers Brick:


  From LEGO fan to LEGO set designer - the Mark Stafford interview


The basic process was:

The position was advertised, and Mark's portfolio was sent in. He was then invited to a two day recruitment workshop along with a number of other candidates.

I've also read other interviews such as this one from The LEGOLAND Discovery Center asking about how Alex Bidolak became a LEGO Master Model Builder, and he came in through the competition route.