Write down the integers you intend to multiply on a piece of paper.
Check if your answer will be positive or negative. Follow these basic rules: Positive times positive is positive; negative times positive is negative; positive times negative is negative; and negative times negative is positive. Or, more simply: Two like signs are positive, but two unlike signs are negative.
Multiply your numbers together. If your integers are low, such as 3 and 9, you should do this by hand: 3 * -9 = -27. If your numbers are high, such as -154 x -270, use a calculator to speed up your process. In this case, your answer will be 41,580.