What is the best way to learn how to play video games?
How could I find somebody who would be interested in teaching me playing games on a fee for service basis?

"Video games" covers so many different systems, from solitaire mouse training to World of Warcraft and Red Cell online worlds. I'd suggest you start small, playing tutorials against the computer in freeware games. Google "freeware games" and take your pick.

I just memorize the controller buttons. Nintendo is the best! If you are wanting anything about computer games, forget what I just said...

Try searching for something local. You really need to practice to get better. Fighting games, especially, are a nice place to get up your video game skill, since they involve such complex balances of reflexes, strategy, and muscle memory.