From Braingle's FAQ:
You must have a high score and have some high quality teasers approved to the site before become an editor. Additionally, you should participate in the message boards, report duplicates, correct teasers and generally prove to us that you want to be an editor. Editors are hand picked by the current editors based on their participation in all areas of the website. A good candidate will not need to ask us to become an editor. If you participate in all areas of the website in a productive manner we will notice you.
Hope that helps!