Modern operating systems do not give you direct access to hardware RAM and instead abstract it in so called virtual memory, which it maps to RAM on demand. Each process is usually given its own private copy of the complete address space. This allows the OS to move a process’ memory around in RAM at runtime or even swap it out to disk. This happens transparently, i.e. a process is not notified of such a relocation and needs not have code to handle this. (Some real time applications might use techniques to prevent having its memory swapped out).
When linking object files to an executable or a dynamic library, the linker statically allocates memory for the cpu instructions of a function/method and for all global variables. When the os loads the executable or dynamic library, it maps this pre-allocated memory into real memory.
On startup, each thread receives a private memory area called the stack. Each time you call a function/method, the compiler inserts code to automatically allocate (by incrementing the stack pointer) enough memory from the stack to hold all parameters, local variables and the return value (if any) the function/method uses. If the compiler determines that it is sufficient to leave some variables in processor registers, it does not allocate memory on the stack for it. When the function/method returns, it runs code generated by the compiler to free (by decrementing the stack pointer) this memory. Note that the destructors of any objects on the stack will be called when the block they are defined in exits, which might be a long time before returning. Also, the compiler is free to reuse the alloacated memory as it sees fit.
When an exception is thrown, the compiler compiler inserts special code that knows the layout of the stack and that can unwind it until finding a suitable exception handler.
As opposed to this, memory on the heap is allocated using new / delete, for which the compiler inserts code to request or release memory using a system library.
Please note that this is a simplified description to give you an idea of how memory allocation works.