NASA's Lunar Atmosphere and Dust Environment Explorer (LADEE) mission was both a lunar science and a technology demonstration mission. The goals identified for LADEE were to determine the composition of the lunar atmosphere and investigate the processes that control its distribution and dynamics, and to determine whether dust is present in the lunar exosphere and reveal the processes that contribute to its sources and variability. LADEE was also developed to serve as a platform for the Lunar Laser Communications Demonstration (LLCD), which had the goal of demonstrating the viability of high-speed optical communication to and from the Moon. LADEE met all of these objectives by operating a robotic spacecraft in a low-altitude, near circular, near equatorial lunar orbit where remote sensing and in-situ instruments measured the Moon's atmosphere and dust environment, and the LLCD demonstrated optical communications at lunar distances. The spacecraft was launched in September of 2013, and spent approximately one month in a transfer orbit before being inserted into lunar orbit in October. It orbited the moon for 188 days, logging time over five lunar synodic months, i.e., "lunations", before being decommissioned via surface impact in April of 2014. LADEE exceeded its baseline mission duration by greater than 40% in terms of time in the science orbit, and greater than 200% in terms of science data return. This paper summarizes the LADEE mission architecture and describes the operational phase of the LADEE mission in detail. The combination of an aggressive science campaign, the demonstration of a new optical communications payload, and the first-use of a new low-cost spacecraft bus resulted in an operational phase filled with challenges, both planned and unplanned. We explain our approach to orbit determination, maneuver planning, attitude planning, activity planning and command sequencing, which yielded exceedingly positive results in the face of a demanding operational timeline consisting of hundreds of interleaved instrument and spacecraft activities. In addition, we discuss the team's identification of, and response to, several in-flight anomalies including a shutdown of the spacecraft's reaction wheels immediately following launch and an on-going unexpected behavior of the on-board star-tracker and attitude state estimation system. Finally, we reflect on the operations experience overall, the successes that LADEE enjoyed, and some suggestions for future lunar missions.