Be at the help sections, participate in discussion threads, don't be a faggot, have some good experience on this site, prove that you can contribute well in a mature manner, know how a job works, and try your hardest.
Long way to go for me, still.
Donator since 09162011
Minion since 10102011
Minion+ since 01062012
Moderator since 08082012
Global Moderator since 10062012
Editor from 06142011 2014
1. Find a section you like.
2. Be active and helpful as fuck.
3. Wait for @Liz to notice you.
4. When a minion is needed, there will be a thread stickied in the section.
5. Apply, and if you did everything correctly, you will find yourself with a shiny new tag.