Okay so there are two general pathways:
1. Users PM members of senior staff.
2. Members of current staff recommend someone.
We look for people who have been around awhile, post helpful information, stay out of trouble, and seem easy to get along with and likely to stick around for awhile. It takes a bit of time and effort to "train" mods, and we are all volunteers so the longer people stay around the easier my life is. Especially now that I am the only Blue mod in all of PA (which is a huge).
After the recommendation or self-recommendation we look at our needs at the time and discuss with the entire staff (or those who give input).
I think we have over 100 volunteers on the site so getting info from all of them is hard (and unnecessary) but most if not all of the Red+s will give input on the nominations as well as many of the assistants (who are the ones on the forums the most and know users best).