Wearing a cover for the first time should be a pretty relaxing process that comes about from mastering simpler foundational steps such as getting them used to the rope touching their behind their hind quarters and around their stomach and rubbing them all over their body.
I like to start with a show or fleece rug as they don't flap or make loud noises, before progressing into a show sheet and then a synthetic or canvas cover. When letting a horse go in a paddock with a cover on for the first time, the cover should have two back straps (rather than one strap underneath the tail) to prevent it from slipping if the horse rolls.