If I want to use a library, I check the following things in the given order:
- Description of the library ("What was it made for?")
- License ("Am I allowed to use it?")
- API documentation ("How to implement it specifically?")
- Example code ("How easy is it to implement? / Get the gist of how to use it")
- OPTIONAL: Unit tests
As an example, take a look at one of my better documented modules: Node-Mod-Load (comments for improvements welcome :) )