How does "sizeof" determine the size of an array?

How does C find the size of an array at runtime? Where is the information about the array size or bounds stored ?

sizeof(array) is implemented entirely by the C compiler. By the time the program gets linked, what looks like a sizeof() call to you has been converted into a constant.

Example: when you compile this C code:

#include <stdlib.h>
#include <stdio.h>
int main(int argc, char** argv) {
    int a[33];
    printf("%d\n", sizeof(a));
}

you get

    .file   "sz.c"
    .section        .rodata
.LC0:
    .string "%d\n"
    .text
.globl main
    .type   main, @function
main:
    leal    4(%esp), %ecx
    andl    $-16, %esp
    pushl   -4(%ecx)
    pushl   %ebp
    movl    %esp, %ebp
    pushl   %ecx
    subl    $164, %esp
    movl    $132, 4(%esp)
    movl    $.LC0, (%esp)
    call    printf
    addl    $164, %esp
    popl    %ecx
    popl    %ebp
    leal    -4(%ecx), %esp
    ret
    .size   main, .-main
    .ident  "GCC: (GNU) 4.1.2 (Gentoo 4.1.2 p1.1)"
    .section        .note.GNU-stack,"",@progbits

The $132 in the middle is the size of the array, 132 = 4 * 33. Notice that there's no call sizeof instruction - unlike printf, which is a real function.