Always remain calm.
A teacher is very important, but I don't feel like starting another "you should get a teacher" rant right now, so I consider the warning as given.

Pay attention to your body's movements, not only to what you are playing. The less you move, the more efficient your playing will be, especially at high speed. Try to avoid unecessary flourishes and keep movement to a minimum.
Always try to be aware and in control of what you are doing, never cheat or rush through a passage.
Keep a steady tempo, do not accelerate. That is a natural tendency that must be fought. The metronome is your friend, especially useful to build up speed while keeping clarity and regularity.
Do not be ashamed to begin slowly. Value accuracy and control over speed at all times.
I start most pieces at a very slow speed, only raise the tempo on the metronome when I'm sure everything is controlled.
Another beginner problem I usually notice is that they use the entire weight of the hand when using the pinky. It looks really painful to me and it ruins control and evenness. Bend your pinky and use it like any other finger. I think a good exercise is to keep your hand completely immobile while using the finger on the key, that should give you the picture of how to do it. It takes a while to get used to it.
Use your forearm in rotating motions when necessary, if you are playing something like C-G-C-G-C-G use your forearm to rotate your hand,not the fingers. The forearm muscle is a lot stronger and the movement willl be more efficient.
Try to keep a relaxed wrist.
Try to identify, isolate and solve your problems. Do not be contented in playing the piece over and over from beginning to end.
Be patient, there is no "end" to the study of a piece. I spent over a year in some and they are still not perfect. They actually never are, you can always do more.
Always remain calm. That's important enough to be said twice. The more relaxed you are the better you play.
And the golden rule:
If it hurts, STOP playing.
Try to figure out what you are doing wrong then start only when it stops hurting. That will avoid all sorts of nasty injuries.
This is what comes to mind at the moment.
I'm not a teacher so if any of you wise people wish to correct any misconception I have feel free to do it.
