First of all, be sure to tighten your girth in at least three stages over a period of time. 1. Secure the girth to keep the saddle up their on its own. 2. Do last minute pre-ride activities (i.e. Stetch your horse's front legs, put the bridle on, pick the feet, put your spurs on, etc.). Then tighten the saddle up a bit more. 3. Warm up on the ground on the lunge, or in the saddle for a few minutes, and then tighten one more time.
Doing this will ensure that your horse isn't being rudely jammed into a tight girth without warning. This might remove some of the stress t that causes dancing. I am guilty of not always following these steps, and instead rushing, and I can tell that my horse gets a bit dancy about it.
Second, to teach your horse to stand while being saddled, the best way that I have requires a round pen or other small enclosure. Bring your horse into the round pen and remove the halter. Use a lunge whip or to create a driving pressure behind your horse (no need to touch horse with whip). Drive your horse in a couple of circles one way, cut them off, drive them the other way. Ask for a whoa, and if the horse doesn't stop and look at you, or better yet, walk to you, drive him some more, switching directions and amound of the circle being driven. When you get to where you horse whoa's and walks up to you, pat him, praise him...During this exercise, remove driving pressure anytime your horse shows the littlest effort to do what you want...he will eventually figure it out. Do this for several sessions until your horse automatically turns to you and stops when you say whoa.
Next, bring horse into round pen, also bring saddle into the middle. Do a short 1-2 circle session each way, ask for whoa, then approach and put on the pad. If he moves, drive him off for a few circles each way, ask for whoa, try again. Repeat until he stands still on his own. Next put the saddle up there, if he moves a foot, drive him off for a short session, try again. Repeat until he stands while you place the saddle, and secure it (not too tight).
Note: when doing this, your horse should have no halter on and be restrained by you in no way. You are teaching him/her to choose to do what you are asking rather than choosing to exercise.
Also, you might want to use a pad and saddle you don't care much about, because when you drive him off quickly, they will end up in the dirt.
This round pen exercise teaches your horse to stand still for you, so can be used for stirrup adjustment, putting on boots, and other activities. You can even use the same concept for bridling, but in that situation, you would have him lower his head by teaching him to move away from light pressure you apply to the poll, and then drive him off and have him work any time he raises his head up high when you try to bridle.
Good luck :)