You are naming three totally different things with "putting".
A class cannot be used by a service (if you mean a ROS service), you need to provide a service server implementation.
Regarding "putting" in the sense of file location:
If other packages besides the one you are implementing are using the class it is good practice to put the header in include/mypackage/header.h, and include the file in your sources via #include "mypackage/header.h". In that case you should also take care of exporting c++ directives in the manifest.
If the header file is only used in the package you can put it in src/.
The .cpp files usually go in src/.
Regarding CMake, in most cases you don't need to put the headers in there.
If you create a new package the CMakeLists.txt already contains the commands for creating a library and exectable, you just need to uncomment them.
Can you be more precise on what exactly you are doing, give a minimal example and say what doesn't work (i.e. what means "cannot use it" for you, give the error messages)? Are you working in the same package or are you building a library package that you want to use in other packages? In the second case you need the export line in the manifest, but the term "-lros" is the linker directive for this package, i.e. instead of "-lros" it should be "-lmylib".
If class.h and class.cpp are in src/ and you have another source file in src/ you should be able to include and use class.h without a problem. If class.h is in include/mypackage/class.h, you should include that file using #include "mypackage/class.h".
