A next-generation lunar laser-ranging apparatus using the 3.5 m telescope at the Apache Point Observatory in southern New Mexico has begun science operation. The Apache Point Observatory Lunar Laser-ranging Operation (APOLLO) has achieved 1 mm range precision to the moon, which should lead to approximately 1 order-of-magnitude improvements in several tests of fundamental properties of gravity. We briefly outline the scientific goals, and then give a detailed discussion of the APOLLO instrumentation.