To subtract integers, add the opposite. For example, 5 - 3 becomes (-5) + (-3) which is (-5) - (3) or (-5) - (-3). The document provides examples of subtracting integers with positive and negative numbers, such as (-12) - (-3), (12) - (-3), and (-7) - (-5). The key is to change the subtraction problem into an addition problem by changing the sign of one of the integers.