How do you teach your horse to sidepass First lets make it easy for the horse to understand the concept of walking sideways by having him practice with you working with him from the ground. Have him in a halter with a 12 foot lead rope and line him up so that he is perpendicular to a fence. Lets have him move sideways to his right so you will then stand on his left side facing his side with the lead rope in your left hand and a stick or a dressage whip in your right hand. Now wiggle the rope up and down lightly at first and then gradually increase the intensity until your horse move his front feet away from you. At that point stop wiggling.
At this point he probably is at a 45 degree angle to the fence with his head farther away from you than his rear end. Now with the stick lightly tap his hips so that his hips move away from you. Now I bet he is looking at you because his hips moved farther away than his front end. So wiggle the rope again to get his front feet to move away from you. You probably got the idea now. Wiggle the rope to get the front end to move away and tap his hip to get the hind end to move away. Alternate between the two but do not do both at the same time but you can wiggle the rope once, then tap once, then wiggle once, tap, wiggle, etc. Have him only move a few steps at a time and then stop and relax and pet him.
When he starts moving both ends easily try just tapping your stick on the ground in front of you about where your stirrup hangs. If he moves nicely away sideways then great. If not you can go back to alternating between wiggling the rope and tapping his hip with the stick. Once he moves both ends nicely with just tapping the stick on the ground then the next stage will be to have him stand there and place the end of the stick in the middle of his side and lightly press. Allow him to learn that a press here means to move sideways. If he doesn't move sideways then go back a step to just tapping the stick on the ground.
Hopefully now he understands about pressure on the middle of his side means to move sideways so you can now saddle him and get on to try it. Still have him facing a fence and then with you sitting there turn your hips as you look to the right so that your entire upper body is facing towards the right. Place your left leg against his body with your left heel lightly pressing against him too. Your right leg will be moved away from his body completely in the direction you want to go. Use a direct rein to tilt his nose slightly to the right if he hasn't started moving in a few seconds of applying pressure against his side. He then most likely will step with his front feet first. If he gets to the point where he is at a 45 degree angle to the fence with his front end leading the way then drop the rein and move your left heel back to ask his hips to move over till he is squared up to the fence again. Repeat this till he has moved about 10 feet then give him a break.
Repeat the above for moving sideways to the left but make sure he moves easily from the ground going both directions before you practice it under saddle. Make sure you pause after he takes a couple of steps each time to give him a reward for figuring out that is what you want. Pet him a lot too. After several sessions he should move easily under saddle for you and then you can practice it without using a fence as a barrier from going forward for he will know that sideways is what you want.