There are widely varying philosophies about the best way to effectively practice a musical instrument, but when it comes to learning challenging piano songs I've found that a sectional approach works quite well. Here's the process I use:
1) Choose an enjoyable song because otherwise this process won't be worth the effort!
2) Site read through the song to get a feel for the material.
3) Divide the piece into sections. The best way to break it up will depend on the song--the patterns it uses, the difficulty of each section, the pagination, etc. I usually end up with sections of between 4 and 8 measures.
4) Set a tempo goal for the entire song (or for various passages if the song contains tempo changes).
5) Start working through a section at a time (in any order). Figure out the best fingering and smooth out trouble spots with frequent repetition. Be sure to use the same fingering every time to aid muscle memory, and practice difficult sections one hand at a time before playing with both hands simultaneously. Learn each measure in the section separately if necessary. Choose a starting tempo that is slower than the tempo goal and play through the whole section until it is smooth and repeatable. Then, using a metronome, gradually increase the speed. Repeat the section as many times as needed until it can be reliably played at the correct tempo. Try playing the section 3 times in a row without making a mistake, then 5 times and finally 7 times. The goal is to get to the point where you can play it correctly every time. Practice daily to retain muscle memory and mental clarity, and periodically play through sections you've already learned to make sure you haven't forgotten them.
6) Once each section can be played at the right tempo, focus on the transitions from section to section and play them until they are as smooth as the sections themselves.
7) Combine sections to form longer and longer passages until you can play through the entire song fluidly. Set high standards and use repetition to reinforce learning. Refocus on trouble spots as necessary.
8) If this piece will be a repertoire piece, play it regularly (once or twice a week) so it stays fresh.
This process can take several days or weeks, depending on the difficulty of the song, but I've found it to be very effective. As an amateur musician I don't strive for absolute perfection, but I like to get as close as I can and this practice method makes it possible for me to thoroughly enjoy my favorite hobby.
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