If you can already pick out a tune - that's actually the hardest bit so you are more than halfway there already!
The left hand plays more notes but they are in incredibly simple patterns, so they are quick to learn.
My method will show you the way that Paul McCartney and John Lennon played piano (and the way most professionals play) and the beauty is you don't need to read a note of music.
Check out this free video workshop: https://decplay.com/seniors-workshop/