Before you even think about riding a travers (haunches-in), you first need to develop a proper straight leg yield and be able to do counter changes (aka "zig-zag") without losing your rhythm, suppleness and keeping a good contact. Then you need to teach your horse about shoulder fore and shoulder in where the haunches travel on a striahgt line (legs not crossing) and the forehand bends around your inside leg to the inside of the arena (the front legs will cross). The dergee of this bend to the inside determines how many tracks your horse is on and thus whether you are doing a shoulder fore, school shoulder in or true shoulder in. If there are 4 tracks with the order of legs being outside hind-outside fore-inside hind-inside for then you are a shoulder fore. With only three tracks visible (inside hind covered by outside fore) you are in a school shoulder in and finally another 4 tracks (outside hind-inside hind-outside fore-inside fore) you are in true shoulder in. Keep in mind also that this movement requires the neck to becoming straight out of the shoulders! The horse should not jack-knife and only neck bend.
Once you have your shoulder-in figured out then you can start to school travers. In this movement the forelegs travel on a straight line (do not cross) and the quarters of the horse bend around an inside leg. The goal is again to work up to being able to maintain a 4 track (ouside fore-inside fore-outside hind-inside hind) travers. Before your horse can do a 4 track travers easily, even a very shallow half pass is not possible.
To change your travers to a half pass, ride on a diagonal line and perform a travers so the horse is parallel to the wall (the haunches should not "lead"). The horse's forehand should be kept on the diagonal line, while the haunches bend around to the dergee in which the body is nearly parallel to the long wall. In the steep half passes (K-B or even K-R) performed in upper level classes, the horse's haunches are bent around to the point where performed as a travers the horse would be at a 60-70 degree angle from the wall.
Good luck! And a website with some very good illustrations ::: Sustainable Dressage - Collection & Its Evasions - Lateral Movements & Their Use :::