Oh, sorry, I misunderstood your question.

The Fortran 77 way is this:

subroutine callit (func, arg)
external func
integer func, arg
print *, func(arg)
end subroutine callit

When you call callit and pass your own function as the func argument, callit will call your function.

The Fortran 90 way is this:

subroutine callit (func, arg)
interface
  integer function func (arg)
  integer, intent(in) : arg
  end function func
end interface
integer, intent(in) :: arg
print *, func(arg)
end subroutine callit

This is wordier, true, but it provides more information to the compiler.  In particular, if callit is in a module, the compiler can check to make sure that the function you pass has the correct interface.

There's a Fortran 2003 way as well, with the new PROCEDURE declaration, but that's for another day.