Do you have to report a ton of posts?
In general, yes.
Do you have to apply?
No and I think this is generally considered a bad idea to do so, though maybe that changed with Mitchell aka bitcoininformation (but see my point about local mods below).
Are you just selectively chosen?
If you report a lot of posts accurately and display a good understanding of the rules and are a very active community member this will greatly increase your chances of getting asked.
I see a lot of staff members who are less then a year old here on the forums and only have a couple hundred posts and you see people with thousands of posts, long time trustworthy members and not staff status or ever mentioned being offered such. Just wondering how they are chosen? For example:
https://bitcointalk.org/index.php?action=profile;u=210680has been here for a year and only 600 posts. Yet staff already??
It's certainly seemingly easier to become a local mod ie one of the local language board mods such as Mitzie is (though not discrediting him for that), though again this depends on other factors like how active a person is and how much a mod is needed for that specific section.