To become a Muppeteer follow these steps:
1) Practice, practice, practice...
2) Write scripts, perform, build puppets (keep doing step 1)
3) Get with a company or make your own (continue step 1)
4) Make an audition tape and sent it to the Jim Henson Company with what they ask for.
http://www.henson.com/employment.php (still do step 1)
5) Get hired
6) Never stop doing step 1.
That said, there is also the "right time, right place" possibility. (This lucky option still requires step 1.)