To me, a good API is something that maps a thought-space onto a problem-space without significant overlap or underlap. It's a translation between the way people think about something and the way a computer needs to be told about it.
As for how you come up with it? I don't think there's a formula for the next good API. I do think we can discuss characteristics of good APIs, though. In fact, this is exactly what the Perl6 language discussion is all about - a good API. And, from following those discussions, I think the most important thing an API designer can have is extensive experience in the problem-space. That and an obsessive-compulsive drive for simplicity. (Sorry, TimToady. *grins*)
We are the carpenters and bricklayers of the Information Age.
Then there are Damian modules.... *sigh* ... that's not about being less-lazy -- that's about being on some really good drugs -- you know, there is no spoon. - flyingmoose