The exact strategy for LES guidance no doubt varies quite a bit. However, the top priority is going to be getting distance between the aborting launcher and the crewed spacecraft, and then keeping that distance. If the launcher is going straight up, or nearly so, when the LES is activated, it's a good idea to not accelerate straight ahead, because after your LES runs out of fuel, the launcher might still hit you. Keeping a modest angle of attack for the departing crewed pod is an important secondary goal.
For Apollo/Saturn in particular, there were three different LES abort modes. First was one-Alpha; this used a sideways-pointed "pitch control" rocket motor to turn the escaping command module out of the path of the booster. Above 3km altitude, mode one-Bravo was used; at this point the rocket was pitched over sufficiently that the command module and launcher would wind up on significantly different trajectories without the pitch motor -- the launcher and spacecraft would be accelerating at different rates in one direction, while gravity was pulling them in a different direction. For one-Alpha and one-Bravo, canards at the top of the LES assembly would deploy after the motor ran out, causing the CM to rotate into a bottom-end-first attitude, which was required in order to deploy the parachutes safely. Above 30km, the air was too thin for the canards, so the CM's RCS thrusters would be used instead to orient the capsule for parachute deployment.
Note that the broad, blunt base of the Apollo command module provided excellent passive aerodynamic stabilization during the LES burn, acting like the tail of a badminton shuttlecock to keep the CM-LES assembly pointing generally into the airstream in spite of the pitch motor trying to tilt it. The Soyuz payload shroud uses a set of grid fins in the same way for passive stabilization of their LES.