Orbital mechanics...the idea of landing on the Moon, without having to worry about atmospheric variables actually makes the problem of landing easier.

About opposite where you want to land, they fired the LM descent stage engine briefly. This lowered the opposite side of the orbit to ~50000 feet. As the LM approached this low point (apoapsis) they turned on the engine again, to slow their forward speed across the surface, and also to control their descent rate for landing. It was this final long burn that brought them to the surface.

They had landing radar to give them velocity and altitude information, and know the geography of the landing zone better than I know my own driveway.

It was math and physics at wotk, real rocket science stuff...and it does work.