Here's a neat example of liberty work, in this case performed by Rex Peterson and one of his horses, Tuff, who is used in a lot of movies. Rex uses whips to cue the horse, because on film sets he often needs to be at some distance from the horse, out of sight of the cameras. Tuff, and other movie horses, are trained in particular to go to and stand on certain "marks" (in this case a raised box, but it can be something small on the ground, too), and then go from one mark to another, or from the mark to the trainer. In a movie that would make it look like the horse was standing somewhere by himself and then came running towards the camera. Or, if the actor cannot ride well, the same technique can be used to make it look like the rider is galloping down the road under control of the rider, when in fact the trainer called the horse to come to him and the actor just hangs on and smiles!
You can read more about Rex's work training movie horses at this site. He's recently come out with some trick training videos, which yours truly was involved in producing.