Write down one of the two digit numbers that you are multiplying. Write the other number underneath the first one, with the digits aligned. The digits on the right of each values represent the ones place, and the digits on the left of each value represent the tens place. Draw a line underneath the second number.
Multiply the ones digit of the bottom number times each digit of the top number. For example, if you have 45 x 75 (with 75 on the bottom), you would multiply 5 times 5. Since this product is 25, you will place the 5 underneath the answer line, in alignment with the ones column. "Carry" the 2 by writing it in above the 4 in the tens place of the top number. Multiply 5 times 4 to get 20, and add the 2 that you carried to get 22. Write this to the left of the ones column. Therefore you would have 225 under the answer line.
Multiply the tens digit of the bottom number times both digits of the top number. First place a zero under the ones column of your previous answer. Then in this example, you would multiply 7 times 5 to get 35. Write the 5 underneath the tens column of your previous answer, and carry the 3 to the tens column of the top number. Then you would multiply 7 times 4 to get 28, to which you would add the 3 that you carried to get 31. Therefore you would have the number 3,150 underneath the 225 from Step 2.
Add the products from Steps 2 and 3 to find the final answer. In this case, you would add 225 and 3,150 to get 3,375.