Success at the piano, to a large extent, is determined by getting the process correct. It has much more to do with developing good habits than it does with intelligence.
Having said that, here are some points to keep in mind:
1) Be *ear oriented*
Successful students want to know how something sounds. They get as clear a picture as possible of what they are trying to do at the piano in terms of sound, and then work to create that.
Unsuccessful students try to do the reverse. They will analyze what is happening in terms of note names and intervals and try to move their fingers accordingly, without first asking themselves how a certain thing ought to sound.
2) Automatise
Successful students have a policy of making things as easy as possible. They do this by repeating things until they are automatic. In doing this, they free up mental energy for other playing tasks.
Unsuccessful students try to handle everything at once. For instance, they will try to play a piece of music before they are comfortable naming the notes of the keyboard or reading music. They then wonder why its so hard to think about the notes, the letter names, hand placement, AND read music all at the same time. Often they feel like they are not smart enough, when in reality they simply haven’t taken the time to automatize the basic elements of piano playing.