Largely automated. Flying the rendezvous by hand on the LM's own resources would have been incredibly hard, although flying it semi-manually with assistance from ground tracking and computers would, in theory, have been possible and the astronauts were provided PADs (lists of times, orientations, etc. for pre-calculated maneuvers) for this eventuality.
The LM ran a series of programs, using data from its own inertial guidance, and a rendezvous radar which measured the distance, radial velocity, and direction to the CM. The programs first got the LM off the ground and into a safe lunar orbit, then performed a series of phasing and plane-change maneuvers to match orbits with the CM over the course of about two orbits. The initial ascent to orbit was performed using the APS engine, and allowed a fairly wide margin for error; all of the later rendezvous maneuvers were performed using RCS, and involved delta Vs on the order of a few meters per second.
The CM had its own matching set of programs that computed the maneuvers from the CM's point of view, using its own instruments. While for the most part, the output of these programs was mostly used as a double-check on the LM's navigation, it was possible for the CM to "swoop in" and rendezvous with an LM that was unable to maneuver, once the LM had reached orbit. This never actually occurred.
All of the programs I've mentioned ran on the primary computer (aka LM Guidance Computer or Primary Navigation and Guidance System), but the LM also carried a second computer, simpler but in theory more reliable, called the Abort Guidance System, that was capable of carrying out these maneuvers.
The computer programs would bring the LM to within about a mile of the CM at a small closing velocity, at which point semi-manual control begins, with the computer maintaining an orientation pointing towards the CM, and the astronaut using data from the radar as well as eyeballs to bring the LM to rest a few feet away from the CM. The CM then maneuvers by hand and eye to dock with the LM.
This essay on Lunar Orbit Rendezvous on the NASA Apollo Flight Journal provides a lot of useful information.