Base your lesson fees, at least in part, upon what lessons are going for in your area. In general, standard rates for student piano lessons will range between $10 and $30 for a half-hour weekly lesson, but you'll want to stay competitive with what's typical where you live. Price range is as of 2009.
If you know any local piano teachers, ask them about rates, as this is usually not considered an impolite question (piano teachers in an area benefit from keeping their rates more or less consistent, so communicating about this is pretty normal). Otherwise, call local piano studios and music stores offering lessons and ask about their rates as if you were considering lessons yourself, but bear in mind that private teachers will often charge slightly less than studios (since studios take a percentage of the fee).
Your piano lesson rates may change depending on your reputation as a pianist and your intended students. Professional concert or orchestral pianists who teach only students interested in becoming professionals themselves may charge significantly more for regular lessons in order to discourage less dedicated students, and because their credentials can command a higher price. Lessons from these types of professionals can range from $40 or $50 to over $100, depending on how much that teacher is in demand. Prices are as of 2009.
Typically, weekly lessons for kids and hobbyist students will be a half hour long, but if you have students who are more serious about their studies, you may give some hour long lessons. You can charge double for hour lessons, or you can give a reduced rate for longer lessons in order to encourage more business.
From time to time, you may wish to adjust your lesson rates in order to do special promotional offers. You may offer free, or half-priced lessons to new students as a way of letting them sample your teaching and see if you're a good match. You may also decide to give reduced rates to students from low-income families.