The Laser Communications Relay Demonstration is NASA's multi-year demonstration of laser communication from the Earth to a geosynchronous satellite. The mission currently has two optical ground stations (OGSs), with one in California (OGS1) and one in Hawaii (OGS2). Each ground terminal optical system consists of a high-order adaptive optics (AO) system, a laser transmit system, and a camera for target acquisition. The OGS1 AO system is responsible for compensating for the downlink beam for atmospheric turbulence and coupling it into the modem's single mode fiber. The mission requires a coupling efficiency of 50%, which necessitates a high-order AO system. To achieve this performance, the AO system uses two deformable mirrors with one mirror correcting for low-spatial-frequency aberrations with large amplitude and a second deformable mirror correcting for high-spatial-frequency aberrations with small amplitude. Turbulence is sensed with a Shack-Hartmann wavefront sensor. To meet its performance requirements in the most stressing conditions, the system can operate at frame rates of 20 kHz. This high frame rate is enabled by the design of the real-time control system. We present an overview of both the hardware and software design of the system, and describe the control system and methods of reducing non-common path aberrations. Finally, we show measured system performance.