I've been on this site since 2012 and I got an email one day from the site. I never asked. They'll find you more or less if they feel you are a good fit.
One suggestion I'd make is to make sure you're as civil as possible with everyone on here and if someone does say something that you feel is inappropriate flag the message and just don't respond to it. Make it a goal to build up a good posting history with helpful information to people without getting flagged by moderators yourself.
Also the "hint" they give in the FAQ is a good indicator of how to be picked also.
"Hint: The success rate of a user's reports is an important criteria to be selected as a Moderator. You can report unsuitable content by clicking on the gray flag from any post. All reports are evaluated by the admins and the success rate on reports by every user is calculated by the system automatically. A user with a high percentage of success rate on reports is more likely to get a Moderator invitation."
According to the FAQ section if you are an active and helpful user they will reach out to you and ask if you would like to be a moderator. I don't think asking for it will help your chances, and doing so might even hurt your chances. I don't know how strict they (the admins) are.
I assume they look for people that go above and beyond the call of duty. Plenty of users are friendly and helpful, but only a handful are moderators.
I will say that all moderators I have encountered so far have been older and more experienced (had more XP points) than you do, so age and experience may play a part in it.
Be nice, report misconduct, answer questions, and do it because you appreciate the site. Usually admins can tell when someone is being genuine and when someone is just trying to become a moderator