Moderators are chosen by higher staff, which includes super moderators, assistant administrators, and staff administrators and are chosen when we believe one is necessary or a current moderator requests additional help. We typically all look for the same thing, but to one of us someone may be perfectly suitable for a position, while to the next, they may not be. It's all very subjective in that regard, but a very objective process. Typically, what we're looking for is active members in a particular forum, who contribute regularly, post original and interesting posts, seem to get along well with people, possess leadership abilities, has a sense of trustworthiness, and someone who we know knows the current rules of a particular forum and reports problems. We prefer someone with no infraction history, or at the very least, at least not any more than two or three infractions, at most. Warnings are usually ignored. There are a few other things that we look for individually, but doing the things I listed is likely to help you much better.
One thing may be important to one of us, but not important to the rest of us. For example, I don't want anyone on staff who has an infraction for disrespecting members, because they're likely to do it on staff, so if I see someone has that infraction/warning, it's an immediate no from me, regardless of how well they perform.