Find a piercing shop in your area certified by the Association of Professional Piercers by using the "locate a member" section of the APP website. This is your assurance that the piercer is properly trained in anatomy and sterile procedure. Mall shops use guns and are never certified by the APP. A doctor may be able to perform the procedure, but your best bet is always to either use the APP website or call tattoo and piercing shops in your area and ask if they are certified.
Call the shop and ask about rates and their policy for piercing minors. By law and APP standards, piercing shops are only allowed to pierce the ears of people over 18 unless accompanied by a legal guardian. Schedule an appointment if you feel comfortable with the information the shop gives you.
Take your daughter to the shop at the scheduled appointment time. Bring along a copy of your ID and her birth certificate. Fill out the disclaimer paperwork giving your permission for the piercer to pierce your daughter's ears.
Ask your daughter if she would like you to go into the piercing room with her to provide support. She may be nervous and in need of someone to hold her hand, or she may want to prove her independence and undergo the procedure alone.
Listen to the piercer's aftercare instructions and ask questions if you are unclear on any of it. Go over the procedure with your daughter on the way home to make sure she knows how to properly care for her newly pierced ears.