Rembrandt Lighting
Named after the Dutch painter, this style of lighting is characterised by a small, inverted, triangle of light on the model's cheek. This will be on the opposing cheek to the light source. This triangle should technically be no wider than the eye and no longer than the nose of the subject.
This style of lighting works well for subjects with round or full faces. This is because it slims the face by lighting one side dominantly and adds definition by bringing out the lines of the cheek bone. Subsequently, this wont be as flattering on models with narrow faces.
Basically, this lighting method is set up using a single light that is set at roughly 45 degree angle to the subjects face. To ensure that the triangle is correctly placed, the light should be slightly higher than eye level.
Loop Lighting
Loop lighting is characterised by the shadow the nose creates 'looping' onto the subject's cheek. It is important to note that this shadow is not directly below the nose and that the area between the upper lip and nose remains lit.
This wil suited to subjects with oval shaped faces as it will lengthen the face because of the downward angle of 'loop'. As a result, it can also give that the appearance of slightly higher cheekbones.
Again, this method is started by using a single light at roughly a 45 degree angle, but in this case it will more than likely to be reduced to a smaller angle to produce the smaller scale shadow. So that the shadow falls away from the nose, the light should be higher than eye level.
Rim Lighting