As I understand it, you work from front to back when putting a rug on, and back to front when taking it off ...
So, to put a rug on, fold it in half widthways inside out, and place the front end over the horse's neck/withers with the fold towards the back. Fasten one chest strap then unfold the rug and slide backwards into place. Fasten both belly straps (crossing them over so the back strap attaches to the front buckle and vice versa), then both leg straps (each fastens on its own side, the second strap passing through the first between the horse's back legs), and/or pull the tail through the fillet string. Then go back to the front end and fasten the other chest strap.
To take a rug off, first undo one chest strap, then any leg straps, then belly, then the other chest strap. Fold the front end of the rug over towards the back end, and gently slide off the horse. It's also a good idea to refasten the leg straps to the rug, and knot the belly straps together after you undo them, to avoid getting anything tangled or whacking the horse with them.
Putting on & taking off a rug is not without risk, but to minimise this it should ideally be done in a sheltered place with the horse tied up to string.