If you want to build a library that is written in C++ but that can be used with a C program, you must create a C API (application programming interface). To do this, make all the exported functions extern "C". Note that this can be done only for global functions and not for member functions.
If you also want to remove any dependency on the C++ runtime libraries, you should enforce the following coding rules in your library sources:
Do not use new/delete unless you define your own global operators new and delete.
Do not use array new/delete.
Do not use exceptions.
Do not use RTTI.