The Hanon Piano exercise number one is quite easy to learn by ear and goes up and down the piano stepwise. I've had a number of students through the years who have used this exercise in C (as written, this uses all white keys) and then moved it up to C-sharp (starting on a black key, this uses all black keys as well as a few white). This is a great process of getting the sound of each note on the piano under your hands. Your hands, ears, and brain all work together to learn where to find each pitch on a piano. It's a subtle and easy way of introducing yourself to the whole piano as an instrument, from one end to the other. Then if you have a good ear, you have a better chance at picking out melodies and chords, because you've played all the notes on the piano. Simple, and doesn't take years of practice to get a good result!