For most people, if all you want to do is multiply numbers, is reasonable to just forget about long multiplication. You can use a calculator for multiplying numbers. On the other hand, if you’re interested in understanding how long multiplication works, here’s are some videos you can watch.
The same ideas are presented in the form of text and diagrams (without video), in reference 1. You might also be interested in long division, as discussed in reference 2 (video) and reference 1 (text and diagrams).
See also: https://www.youtube.com/watch?v=L0pSxu_ZaNM