Take it slow - By going slowly and getting it right the first time you will save yourself countless difficulties trying to iron out small mistakes that can become ingrained in your playing. Furthermore starting slowly makes it easier to play relaxed and with proper technique, which will translate into smoother playing and ultimately the ability to play faster and with greater precision than if you had tried to shortcut the process by starting too fast.

Isolate Trouble Spots - Instead of playing a piece up to a difficult spot, making a mistake, then starting over to play to the same spot and make the same mistake, take the difficult section out of the piece and focus just on that. work on it slowly one note at a time until all movements are comfortable, then bring it up to speed and play it a few more times at tempo before re-inserting it into the rest of the piece.

Have a Plan - Think about what you want to accomplish when you sit down to practice. A good format for a 30 minute practice might be: 2-5 minutes of warmup / technique exercises, 10-15 minutes on new, challenging material, 10 minutes on older repertoire and favorite pieces, and 2-5 minutes of technical exercises, played faster now that you're limbered up, or just messing around experimenting / improvising and discovering new sounds. Another good suggestion for working on particularly challenging passages is to have a three minute egg timer on the piano. Work on the trouble spot for three minutes and then move on. Even if it seems you haven't made any progress, when you come back to it the next day it will almost certainly be easier.

Remove Distractions - Playing the piano requires concentration. Try to schedule a time when there won't be interruptions and turn off the TV and radio. The more things that take your attention away from the piano the less effective your practice time will be and the slower you will progress. The one exception to this rule is if you are preparing a piece for performance, after you have learned it and worked out any technical difficulties. Then I recommend the opposite. Turn on the TV and radio, alarm clock, etc. This will teach you to focus your mind even in adverse conditions. After all, we know that somebody will cough at the most sensitive part of any performance.

More to come...