Begin each practice session with some scales, arpeggios and other technical works. Then move on to some of your pieces (not songs unless you are playing pop). Work on sections that you have trouble with slowly until you get them, and then move on to others. When you are away from your piano, there are many awesome websites where you can learn things like music theory and ear training. My favorite is https://www.musictheory.net Having a solid understanding of theory is integral to being a good pianist. The best way to maximize your progress, however, is to get a good teacher.
I'll try to give this a shot.It depends on your ambition and your goals.First of all, here is what I did in the first few months: I took a few relatively difficult arrangements of pieces I liked, and learned them. The pieces were maybe at a grade 5-ish level, and I learned them in the first six months. They were arrangements of popular music, which basically had a melody/melody+broken chords/octaves in the right hand, and stride patterns+arpeggios in the left. Think something like Comptine d'un Autre eye from the Amelie soundtrack. Although I may not have learned them perfectly, it was good enough to wow my friends, and that gave me an incredible amount of confidence moving forward.Now, as to what I would have done in an ideal situation:I would have employed a teacher who was a college professor or similar, and was a great teacher who really knew their technique inside out, such as Josh Wright for example, explain that I was a very dedicated student, and would have asked them to teach me. While I did learn quite fast by most standards, I think I could have reached a grade 8 standard in 1-2 years with an excellent teacher, and progressed much further than I have already. But it's never too late to make amends, amirite?If you do end up getting an expert teacher, however, do make sure to still attempt stuff you like on your own. Nothing is impossible -- just have that faith in yourself and intelligently apply what you know. If you think you might be able to learn something, give it a shot for a week. I think quantity matters a lot in the initial stages. I know people who go through 2-4 mini pieces each week at the start. While I didn't exactly do that, I would probably arrange a new song and improvise a lot every week, and while it's unconventional, that trained me knowledge of finger patterns to the point where I could improvise fluently (which requires you to come up with all kinds of configurations on the fly), and quickly come up with a near-optimal fingering solution.I would also learn music theory. A lot of people I know tend to take things slow, but I tend to binge information. So I started a Coursera course on music theory, and tried to get through a week's content every day. Although there were several days in between where I didn't get to it, I learned a lot from that course, to the point where teachers didn't really have to teach me how to analyze normal classical pieces. I would demonstrate that I knew my theory by analyzing a piece, and so that saved me all the time teachers would have to spend on theory.ETA. One summer may also be enough time to learn how to play melodies by ear somewhat fluently. This helps you in a number of ways down the road.EETA. Apologize for the typos. I was typing on my phone and am too lazy to fix them now.
Topic: Making a plan for summer practise 