You need pretty large antennas to send data over billions of miles - and fortunately, NASA has them.
The New Horizons mission operations team communicates with the spacecraft through NASA's Deep Space Network (DSN) of antenna stations. The DSN consists of facilities in California's Mojave Desert; near Madrid, Spain; and near Canberra, Australia. These stations are separated in longitude by about 120 degrees, assuring that any spacecraft can be observed without interruption as Earth rotates.
Visit the DSN Web site for more information.
All commands sent to New Horizons must pass a rigorous development and review process to ensure the safety of the spacecraft. The mission operations team works closely with the instrument, science and spacecraft teams to develop the commands that perform New Horizons' activities. After the command sequences are tested on a New Horizons simulator, the New Horizons Mission Operations Center at the Johns Hopkins University Applied Physics Laboratory (APL) in Laurel, Maryland, sends them to the DSN, which is operated and managed by NASA's Jet Propulsion Laboratory in Pasadena, California.
Data received on Earth through the Deep Space Network is sent to the New Horizons Mission Operations Center at APL, where data are "unpacked" and stored. The mission operations and instrument teams scour the engineering data for performance trend information, while science data are copied to the Science Operations Center at the Southwest Research Institute in Boulder, Colorado. At the Science Ops Center, data pass through "pipeline" software that converts them from instrumental units to scientific units, based on calibration data obtained for each instrument. Both the raw and calibrated data files are formatted for New Horizons science team members to analyze. Both the raw and calibrated data, along with various ancillary files (such as documents describing the pipeline process or the instruments) will be archived at the Small Bodies Node of NASA's Planetary Data System.