> what is the trick behind using two different hands to play several
> different notes with different fingers

I'm very much a beginner at trying to play the piano, so this may be wrong, but afaik there is no *trick*. But there are things you can do to shall we say "ease the pain":

 - I found [this technique][1] very helpful
 - I installed EasyABC on my laptop, then typed in the scores of the simple tunes I want to learn. Then, using the % (comment) sign in EasyABC, I can disable one hand in the score, and have a simple means of playing back to me only the hand I'm struggling with and for which I need a known good sample. EasyABC also lets one change the tempo very easily. As far as this beginner (aged 67 I might add....) is concerned, there's no trick, just plug away at it. (Starting really simple of course: I have Thompson's old material from the 1930s.)

  [1]: https://www.youtube.com/watch?v=cmYRz1adfLk