This information is based on what my piano instructors have told me over the years AND what my new violin instructor tells me. This advice applies to both instruments, so I imagine it may translate to other instruments like guitar too.
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Several short practice sessions each day (20-30 minutes) are better than one long marathon practice session (2 hours). Sloppiness and lack of focus sometimes set in after about 30-45 minutes.
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First – always start with scales (or equivalent exercises).
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Second – practice new songs slowly enough so that your tempo is consistent throughout the piece and you play it without mistakes. If you make a mistake, play that part until you get it right. Once you learn the song better, you will naturally speed up and you’ll play it better and more consistently in the long run.
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Third always have a performance type piece (could be same as practice songs) that you play at the written tempo. It is okay to play through mistakes during this part of your practice.
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Do steps 2, 3 and 4 in each 30 minute practice session.
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Practice tough spots in songs 2 measures at a time. Play the tough part over and over again until it is smooth.
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ALWAYS use correct fingering. Don’t cheat. Fingering only gets harder and harder, and you have to train your brain with the fundamentals.
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Watch out for tension in your fingers, hands, arm, shoulder, elbow, neck, jaw, teeth – remember to relax!
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If you have an instructor stick to what they want you to practice. If you are playing around on your own just for fun, that is fine, but that is not considered practicing per se.
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Music is one skill where practice does make perfect. Some days will be better than others and you will reach plateaus. Stick with it and you (and those listening to you) will be rewarded with beautiful music.
If you are considering learning an instrument as an adult, there is a great book called Never Too Late about a man who learned to play the cello in his 40’s and ended up making it his career!
Good advice. Just a picky bit about terminology: it’s only a “song” if it’s music meant to be sung. If no one is singing, it’s not correct to call it a song. When the music is instrumental, it’s a piece, a composition, a work, a sonata, etc.