Talk to your school counselor. Many programs allow children as young as 16 to shadow a nurse, so ask your counselor if she is familiar with a shadow-a-nurse program.
Contact your local hospital if your school counselor is unable to provide information. You should call the hospital's general number and inquire about shadowing a nurse. You may also be able to contact a nursing association. For example, the Texas Nurses Association provides information for perspective nurses to shadow working nurses and points them to local hospital sites.
Schedule a date to shadow the nurse you are assigned to. Show up on time and stay for your entire shift to respect the time that she is giving up for you.