Secure a job on the movie set or by working with one of the stars. You can work in any capacity on or off the set to get a line on invites for the premiere. Of course, you'll still need to put your request in early or be close to the powers-that-be to get an invite for a big mainstream premiere unless you're close to one of the major stars.
Schmooze with show biz and media types. Even if you work at Wal-mart you can secure invites to movie premieres by hanging out with filmmakers, directors, screenwriters, even secretaries and stagehands. Movie people tend to get blasé about movie premieres, and pass invites to their friends if they're too busy to attend.
Write or take pictures. Be a member of the press, even a freelancer, and you'll get into most movie premieres. Getting into a major premiere like a new Star Trek or Tom Cruise movie takes a bit of effort, but if you persevere, you'll get an invite.
Work at the theater. If you're not currently employed there, check with temp agencies, catering companies and other businesses that send contract employees to work the event. Get your application in quickly enough and you'll get to hobnob with the stars and get paid for it too.
Contact the film's publicist about invites. He or she has access to many invites reserved for press, show biz folks and even fans.
Win a contest. Websites, radio and TV stations and magazines often sponsor contests offering free invites to movie premieres. Some contests include other prizes like limo rides to the event, or a meet and greet with the film's stars.