Pallas Here's how i learn a new song:
First, I pick a song that I like. Then I play through the whole song, as slowly as necessary, to get most of the notes right. Stop a moment to reflect on whether I like the way it sounds, or not. If not, pick a different tune. If I like the tune, or arrangement, I continue on by picking out any tricky parts, not more than a measure or two at a time. Play the measure slow enough to get the fingering right. Then go back two measures and play through the rough part. Then go back four measures and play through the rough part. Then go back to the beginning of the section and play through the rough part. Then, take it from the top and play through the whole piece. If another rough spot pops up, repeat the procedure. Disregard tempo - strive for accuracy. Eventually, depending on the player's technical ability, the song or piece will be learned.
Notice I said, depending on the player's technical ability.
I had formal training for the saxophone, and had played professionally for over forty years. My school band teachers both used the "measure minus, two measures, four measures, section, and from the top method" for private lessons as well as working with the jazz band. Years later, when I played with other jazz musicians, we used the same method to tighten up songs in the group. If a song can't be learned, using this method, to the point of being able to play through in it's entirety, the piece is probably beyond the player's technical ability.
I feel there is little to be gained by attempting to play a piece that is beyond your technical ability. Yes, you want to improve, but this comes gradually by playing pieces you can actually play. And by studying scales and fingerings.
Some of the songs I play on the piano have taken weeks to get to a point where I'm pleased with how they sound. Some have taken months, maybe years, to get to where they are comfortable, where I don't even think about the technical aspects, they just sort of flow out and I can sit back and listen, maybe improvise, and enjoy playing. And, with those tunes, others can enjoy what I'm playing, too.
I don't have a regimented practice schedule; don't keep a record of my progress; don't use a notebook, don't use an app. I have no goals to learn a set number of pieces. I sit down at the piano when I feel like it, and play for as long as a little as I want. When I played regulars gigs, I found that practice actually reduced my performance energy. I don't want my interest in the piano to feel like work or like I'm studying for an exam. There are two reasons I play music - to exercise my creativity and pure enjoyment of the sound I make.
