Geany automatically indexes your open files for auto-completion, but if you want it to index some library or API, you have to create a global tags file like it describes here in the documentation. I have had mixed results getting this to work completely and correctly though.
I used to use Geany on Linux, but I have moved to QtCreator. Even though it has an emphasis on Qt, you can use it on any C or C++ project (you just have to specify your own build process or do it outside the IDE). The editor is one of the best I've used on Linux and the autocompletion works great without a whole lot of configuration. Also check out my answer here on how to set the include paths. Anything in the include paths will be indexed for autocompletion automatically.