After reversing one of the numbers and writing it below the other number, the method essentially involves four steps  that   has to be done repeatedly. They are,

1) Multiply digits that fall in the same line.
2) Add the products thus obtained in the previous step. This sum is added with the carry, if any, from the previous stage.
3) Write  the least significant digit of the sum in the result column. The rest of the digits form the carry for the next stage.
4) Shift the reversed number to the left by one digit.Goto step 1.

Repeat the above steps until all the digits in the reversed number have crossed the other number.

What is readily visible is that the digits of the answer keep falling in their places (from the least significant digit to the most significant digit) after each step which makes the method easier to do it, even mentally.With a little practice, we can master multiplication of any arbitrary digit numbers using this method.

Example : Multiplication of 5 digit numbers.