There are prodigies who can sit down at the piano and learn effortlessly, but most students must practice diligently to play well. Often students frustrate themselves by trying to do too much at once. Attempting to handle notes, fingering, timing, and expression in both hands at the same time can be overwhelming. However, by dividing the practicing process into a number of manageable sub-steps, you can progress more readily with a minimum of frustration. Below is a method I've found most effective in accomplishing this end.
First divide the piece into practice sections, following as much as possible the phrasing and natural breaks in the music. If the music is relatively easy for you, these sections may be eight or sixteen bars long. If the music is particularly difficult, two or four bar sections may be more appropriate.
Begin in the first section with the right hand. Play the notes firmly, with the correct fingering. If fingering is not provided, write it in if necessary to guarantee you use the same fingering each time, since learning is facilitated by exact repetition.
Don't rush. Pick a tempo that enables you to play comfortably and accurately. Remember if you play a note wrong once, you'll tend to make the same mistake again.. Repeat the notes in the section until you can play them effortlessly and without stumbling. Saying the notes out loud as you play tends to increase concentration and speeds learning.
Once you have mastered the notes and fingering, go over the section again, focusing on playing in time. Repeat the section several times until you can play it correctly. Then go on to the next and succeeding sections, treating each in the same way until you finish the piece. This is concentrated work. You may want to stretch this process out over several practice sessions, if as you tire, you begin to make careless mistakes.
Treat the left hand in a similar fashion.
Don't attempt to put the hands together until you can play each independently, comfortably and in time. Practice sections should again be employed in putting the hands together. It is often helpful to play alternately the the right and left hand parts several times independently before attempting to coordinate them. Counting at this stage is essential to ensure that the parts come together correctly. It's also important to repeat the section several times once the hands are together to consolidate the learning and ensure that there will be a minimum of "learning loss" between practice sessions. This frustrating but common phenomenon can be reduced by maintaining a frequent practice schedule.
Pieces should be taken up to tempo very gradually; rushing the process leads to mistakes that are easily learned and difficult to correct.
Finally, focus on dynamics, phrasing and other performance details to achieve a polished effect.
Sometimes, in spite of careful practice, you may find yourself stumbling at a certain point in the music. If you examine the situation, you'll usually find you're making the same mistake each time- like forgetting to play a sharp, putting one in that's not there, missing fingering, or playing a phrase consistently out of time. I've found the best way to deal with such trouble spots is first to identify exactly what you are doing wrong. Then go carefully over the bar or phrase containing the trouble spot several times, reminding yourself as you approach it exactly what you must do to correct the problem, such as "play G not A" or "count two not three". As you follow this procedure, you'll tend to memorize the correct version and transform it into one of the securest parts of your performance.
To play convincingly, the performer must get beyond the notes and attempt to convey the spirit of the music. In doing so, several factors should be considered: the work's title, tempo, and expression markings; knowledge of the composer's life, times and the performance practices of the day; and most importantly, the performer's own imagination. Imagining dancers will make your waltz more life-like, as thinking of a loved one will render a love song more convincing. The more knowledge and imagination you can bring to a performance, the more effective and communicative will be your style.