It's hard to "just send pull request" with such core and large aspect as documentation. You can work on your own and submit bug fixes, improvements, more examples and clarification for existing docs, but making documentation from scratch requires communicating and planning together with project authors. And you should know the project very well to write docs, at level of core developers.

One of the ways it can be done is to start independent documentation effort, without even considering to merge it to project repository. Then, having these "draft" docs, it will be easier to make "official" documentation. Even blog posts "how to get started with libui" can be useful. This project looks very promising, like WXWidgets, but in C and not C++, for this reason it has lots of language bindings already.