Pierre Normandin followed the path of "well-known AFOL doing tremendous sets" to "AFOL invited by LEGO to participate in secret projects from time to time" to "Actual LEGO designer" (I'd like to say "demigod", but he tends to frown at me when I do that). He was also one of the first groups of LEGO Ambassadors.
But in any case, the most important criteria is, you have to be a tremendous builder. The next step is to make LEGO know about you one way or the other, but if you are a tremendous builder, chances are they will. Then, you have to inquire about job openings and of course, apply. In that respect, I think his path is similar to Mark Stafford's.
LEGOland parks sometimes fill they openings through competitions, but I don't think Billund does that.
Edit: by the way, the job postings aren't in any kind of secret place, but quite easy to find on the LEGO web site (I think they're in category "Product Design/ Development"). Of course if they happen to search for candidates for other jobs in your own area of expertise, maybe being already in house is a good path to reach the designers team, too.