I am trying to get a job as a Stack Exchange system administrator and programmer. Where should I go to sign up for the job?
There is a work here link in the footer of all Q&A sites.
Send your application through that page, go through the interview process and if you pass all interviews, you will get hired.
Do your best to contribute to the community you are finding a job in, like Stack Overflow for programmers. If you have a lot of experience there, run for moderator. Some moderators have been asked to promote to a job at Stack Overflow Inc.
If you don't end up as a moderator, at least your profile has a lot of information you acquired to show your competence in the field, which will give you a job more likely.