Ahh, I guess this is the thread I've heard mention of but couldn't find.
I guess just be a good person, and be around when someone is needed. It's not too often that new people are added as ops. It can be helpful if you know how to do something useful, but not particularly needed. If you're talking about IRC operator, than it's mostly just being around to moderate the channel, and knowing how to do a good job of it. But again, people start complaining when the channel gets too op heavy.
Oh, and what other people would think of the candidate tends to be more important that what the candidate thinks of themselves. Which should go without saying, but still, some people need to be smacked with a large trout in this regards. (I'm not saying anything about people here, but I have seen some people vying for an op position elsewhere and they seemed to be the only person who thought so highly of themselves. (thumbsdown) ) You shouldn't have to tell people you're a good person. They should know you are.
But yeah, generally things are done on a case by case basis as new people are needed. Not so much a set procedure as just some common sense.