The stirrups on an English saddle should be run up the leathers, and the offside stirrup of a Western saddle should be hooked over the horn or folded over the seat. The girth or cinch, if they are attached, should be folded back over the saddle seat. With stirrups and cinch out of the way, they won’t hit the horse as you lift the saddle over the horse’s back.
Lift the saddle high enough that it doesn’t hit the horse or knock the pad out of position. The saddle should be placed slightly forward and settled back. Be careful to place the saddle gently on the horse’s back. Letting a saddle fall heavily onto your horse’s back may cause it to spook or resent being saddled (become ‘cold backed’).