I am slightly confused on how a compiler stores variable on the stack. I read that c++ can store local variables on the stack, but if the stack is LIFO, how could it make sure to call the right variable when the variable is called in the program?
The run-time stack isn't simply a LIFO structure; it's a complex structure which supports random access.
Typically how it works on many platforms is that whe na function is entered, a new stack frame is pushed onto the stack (LIFO fashion). Local variables are stored within the frame and are accessed relative to a more or less stable pointer stored in a register.
When other functions are called, they push their own frames, but they restore everything before returning.
Run-time stacks also typically support the ad hoc pushing and popping of individual values, for the purpose of temporarily saving register values or for parameter passing.
A common implementation strategy for that is to allocate the frame first. For instance if a 512 byte stack frame is needed, the stack pointer is moved by 512 bytes. The stack pointer is then used freely for pushing and popping, provided it doesn't pop too far and start gobbling into the frame.
A separate frame pointer may be used which tracks the location of the frame. The frame is then accessed relative to that frame pointer, which allows the stack pointer to move without interfering with those accesses.
Compilers can generate code without the use of frame pointers also; if the stack pointer only moves in ways that a compiler knows about, it can adjust all the variable references. Over an area of the code where the compiler knows that the stack pointer has moved by four bytes due to something being pushed on it, it can adjust the stack-pointer-relative frame references by four bytes.
The basic principle is that when a given function is executing, then the stack is in the right state that is expected by that function (unless something has gone horribly wrong due to a bug causing corruption or something). The LIFO allocation strategy of the stack frames closely tracks the function calls and returns. Functions that are called must save and restore certain registers (the "callee-saved registers"), which helps to maintain the stable stack environment.