Most melodies consist of notes that is 1 or 2 steps up or down from the previous note. This helps when playing by ear. So hum a melody slowly and pay attention to those small shifts in pitch. Listen if it is up or down, 1 or 2 steps. Nail that, and you'll be picking out tunes fast! The melody can be moved up and down. When you play in C (transpose so first and last chord are C) you can skip the black keys and find right keys 40% easier (7 instead of 12 keys per octave).
To simplify chords for a C chord, take a low C and next C one octave up. Lock the fingers and move the hand to F or G for the other two most common chords. Many songs add E minor and A minor, but a simple way is to play them just the method above, the minor sound is usually crated by the melody notes, so you can simplify.