Arduino libraries are usually C++, if it is a C++ library, I think you must write your project as a C++ project unless you write C wrappers with single instances of the classes you will use.
if you want you can pre-compile the library into an object file and link your project with it, this isn't a good idea since you need to recompile the library if you change your clock speed or chip part number
another option is to just copy the library code files into your project so they get compiled along with the project every time you build your project
if you want functions such as pinMode or digitalWrite to work in a C project that is not meant for the Arduino, you need to modify the Arduino core files and add them to the project, or create a custom core (there's an option in my editor for a project to use custom cores, if you wanted to use a sanguino, or teensy, for example). I don't think this will work well for a C project since the Arduino core uses C++, and already defines a "main" function. You'd need to find the files solely responsible for the functions you need. Also classes can't be used in C.
If you are finding that you need to do things that Arduino can't do naturally, start moving away from Arduino, you'll save a lot of headaches