"Unresolved external symbol" is one of the errors issued after successful compilation, but failure at linking.
.h files are headers. Without them, your project would not compile.
You must have forgotten to add a library. Without them, the project will compile, but not link.
Library files on Windows are usually distributed with extension of ".lib", i.e. "libspotify-2.0.lib", and sometimes they are paired up with DLLs: "libspotify-2.0.dll". File names are artificial. Actual ones may differ.
You must find a proper LIB file that was distributed with the version of libspotify you are using, and then you must edit your the project's options or switches to make it use that library during linking. Assuming you are using MSVC, it's Project->Properties->Linker->AdditionalDependencies. Add the path to the LIB there, and rebuild.
And afterwards, keep your paired DLLs near the final EXE, or else it will compile and link properly just to crash at startup. (Although, there is a type of libraries called "static libraries" that are also LIB files and that does not require any DLLs. You can tell them by the size usually: dynamic LIBs are few-tens of KBs, while static libs are usually hundred-thousands of KBs).