gcc -myCfile.c -lmystuff.a will generate myCfile.o and link it to both our own library myStuff.a (to get myfunction.o) and the default standard C library. This results in an executable file a.out being created. Our header file would have to be in a standard place to be found by gcc.
gcc -c myCfile.c -> generates myCfile.o gcc -c myfunction.c -> generates myfunction.o gcc -o myProgram myCfile.o myfunction.o -> generates myProgram executable