For warm up, it's pretty much like for anything else...ensure they are soft and responding by moving all 5 body parts....using various exercises--sidepassing, backing, spins, etc...then I will walk/trot/lope/gallop around the arena to the left at least two times for each gait, then I will do it to the right(left is always first since you want the horse to "think" left lead always. Then I will lope circles to the left until I feel him relax. Once he does then I will walk him in and out of the box while spinning my rope, and finally I will let him just sit in the box for awhile.
As far as training -- you first have to track cattle(follow them about 3-5 feet to the left and 3-6 feet behind) until the horse will do it on his own. Then you have to move that to the chute...track from the box, while doing the above you need to start "logging" the horse so that it gets used to pulling something with a rope(you can use an old tire or 1/2 of a cross tie for this)--work up to about 30 minutes of pulling the log at the walk and trot; then start steer stopping from the box(rope the cow and then slowly stop the horse until the cow and horse are both standing still); then steer stop and make him "hold" the cow for awhile--when you start steer stopping, start having the horse back while logging(and anytime that there is slack in the rope, make him back until it's tight).
Once you have him good at this you start training for holding the calf while you dismount....but, the above will likely take 2-6 months, once you get that I will then go over what to do next.