Often I've started with some example code that invokes part of the API, but not all of it. Or in C I can give it the .h file, maybe without comments.

Sometimes I can just say, "How do I use the <made-up name> API in Python to do <task>?" Unfortunately the safeguards against hallucinations in more recent models can make this more difficult, because it's more likely to tell me it's never heard of it. You can usually coax it into suspension of disbelief, but I think the results aren't as good.