After completing a lunar survey and orbit, and taking a grand tour of the solar system, Mission 16, named Moon Landing, allows you the chance to make your first extra-terrestrial landing. You'll assemble another Saturn V rocket, this time including the Lunar Module Descent and Lunar Module Ascent vehicles/modules. You'll dock with the assembled Lunar Module in HOM's orbit and fly to LUN where you'll detach the Lunar Module and land on the surface. You must land in a certain parking zone. To successfully land, you must match the rotational speed of the moon. After landing, you must take a picture, then leave the surface, redock with the Apollo Service Module, return to HOM, discard the LM Ascent vehicle while returning to HOM, and splash down.
This contributor recommends starting from orbit in the same direction as the moon (note: the moon rotates clockwise, so enter from the left side of the moon), descend your vehicle to a comfortable distance from the surface, reduce speed to just above the orange zone. As you're passing over the landing zone, wait until you're just about to leave it before you begin reducing your speed to match that of the moon, or you'll miss the zone.