The loop you write here would be:
xor eax, eax ; clear loop variable
mov ebx, limit
loop:
cmp eax, ebx
je done
inc eax
jmp loop
done:
...
I really don't understand what you mean by "increment an array".
If you mean that you want to load some value from one array, manipulate the value and store the result in a target array, then you should consider this:
Load the pointer for the source array in esi and the target pointer in edi.
mov esi, offset array1
mov edi, offset array2
mov ebx, counter
loop:
mov eax, [esi]
do what you need
move [edi], eax
inc esi
inc edi
dec ebx
jne loop