Another way is to have a forward and a backward iterator or even just two position variables. Then one go up and the other go down until the right is now on the left (or they are equal).
Something like this is pseudo code:
1 2 3 4 5 6 7 8 9 10
left = position 0
right = last position
palindrome = true;
for left < right, left increment, and right decrement
if(left != right)
palindrome = false;
break out of loop
now you know if it is a palindrome or not