How to Practice Piano

Work just one phrase, or passage, at a time. Start with a very slow and easy tempo.
Work hand separately, first (if both hands are playing simultaneously in the exercise).
Once you feel confident mastery of each individual phrase/passage, move the tempo up a couple of notches and repeat the process.
Continue working at faster and faster tempos until you start to feel challenged beyond your comfort zone.
(You should always be able to keep the rhythm and the notes even and steady, and keep your arms and shoulders free of tension while you play.)
If you are working on a long exercise, or etude, work on individual passages from slow to fast, and then start stringing them together at slow-to-fast tempos.

Divide your exercise into 1-, 2-, and/or 4-beat “links” (like chain links), or 1-, 2-, and/or 4-measure links. (If playing 16th notes, divide into beats. If playing quarter notes or eighth notes, divide into measures.)
Play each link from its first note to the first note of the next link (thus, linking them together). You will be playing in short spurts, stopping on the first note of each link, and then starting on that same note for the next link. (The first notes always get played twice; the last note of one link is the first note of the next.)
Start with short links, mastering the notes and the rhythm for each link. Use the metronome to help keep it even and steady, starting at a slow and easy tempo.
Expand the length of the links (from 1-beat links to 2-beat links, or from 2-beat links to 4-beat links, etc…), still at the slow and easy tempo.
Keep lengthening the links until you are playing the entire passage, phrase, or scale with no stops, at the slow and easy tempo.
With each phrase/passage, repeat this process over and over, gradually working up to faster and faster tempos on the metronome.
Continue working at faster and faster tempos until you start to feel challenged beyond your comfort zone.
(Rhythms and notes must be steady and even, shoulders and arms relatively relaxed.)

Decide what kind of groupings you are going to use: groups of 3’s (best with triplets), 4’s (best with eighths and 16ths), or even 6’s (good with triplets, or eighths in compound meter <6/8-time>).
- Play the entire run of notes with pauses on the first note of each group. An example of groups of 4’s:
  1—-2341—-2341—-2341—-2341—-2341—, etc…(saying these numbers helps)
  * Next, play the entire run of notes with pauses on the second note of each group:
  12—-3412—-3412—-3412—-3412—-3412—-, etc…(say the numbers while you play)
  * Next, play the entire run of notes with pauses on the third note of each group:
  123—-4123—-4123—-4123—-4123—-4123—-etc…(say the numbers!)
  * Next, play the entire run of notes with pauses on the fourth note of each group:
  1234—-1234—-1234—-1234—-1234—-1234—-etc…(say the numbers)
Make sure that the notes in between the pauses are fast (eventually) and even, and that the hands are exactly together.
Use the pauses (which can be as long as you want them to be, but not too short) to think ahead for the next group of notes, as well as to remind your arms and shoulders to relax.
After playing all of the rhythmic variation once or twice, try playing the rhythm as it should be (with all even 16ths, etc…) and you should find that it seems much easier now.