The quickest way is ask admin about it http://www.girlsaskguys.com/contact They will review your profile and see how near you are the criteria then advise you what you need to do to get offered a Moderator role.
You can become a moderator by being a top user which means posting regularly, logging in daily, and reporting content that you think violates the guidelines. Once you think you've reached that point, then just contact us and we will consider you for mod status. You can learn more by checking out the FAQ :) http://www.girlsaskguys.com/faq/moderators#34
Ask questions, give opinions, learn the posting rules so you don't make too many errors, be kind to other GAGers, re-learn the posting rules so YOU can report anything that's against the rules. It's not hard to do, just keep on and hopefully, you will get recognition. Eventually, you might be invited, like I was.