I've had my piano teacher for almost a year and though shes expensive(100 dollars for one lesson of one hour- she studied at RCM in the 1960s for five years under a pupil of Czerny), shes well worth the money.
I suppose the best teachers teach their students how to teach themselves- the trite old principle of "learning to catch the fish yourself". And this is exactly what she has done for me. When I first went to her after taking grade 8 on my own, i was a bundle of uncontrolled nerves- playing with little arm weight, collapsing finger joints, tense shoulders and tense arms resulting from a tense mind. The technical problems were pointed out to me one by one, with the first most important thing being relaxation of the mind when playing. She taught me the principles of arm weight(how the arm is like a dead thing- dead as in heavy and made me aware of the sensations of playing with arm weight. And then she prescribed Hanon for my collapsing finger joints and the weak third n fourth fingers. She's just so patient and reassuring, though quick to nip any bad habits in the bud.
She also stresses the important thing of REALLY listening to oneself when practising, whereupon i admitted that i'm lazy to do so at times. And of course the music essentially has to come from oneself, though the teacher is there to guide us along. I just started preparing for the dipABRSM piano performing with her a year ago, and one of the pieces is Beethoven's Moonlight. The "stillness" of the first movement is something which demands the utmost concentration and calmness of mind, and I'll always remember her words- that nobody can tell u exactly HOW to play it. Never once, has she stifled my own interpretation and told me the "correct" way to play any piece(perhaps I have some instinct of my own). She does chide me for uneven tone, for not using arm weight, for not concentrating. Really, she makes it seem like ANYTHING is possible as long as I concentrate 100%.
I suppose I have vexed her at times with my hangups of always being excessively self-critical and impatient with myself, to the extent that it seems ive got no trust in her. OH well, we dun pay money to our teachers so that we give them a good time.( just joking, im a teacher myself n i understand the multitude of frustrations)

As usual, people who are really professional and experienced make it seem effortless, and that includes teaching.