Step one is to remove the old chin strap. If it is in otherwise good shape, you could keep it to be repaired professionally. Fasten the throatlatch to keep everything neat and easy to visualize.
Step three is to thread the stirrup leather through the slots and ring. Ensure that the side facing towards the horse is the same side that you would like to show on the outside of the finished chin strap (thread it wrongly and your buckle won't be able to close). You can trim off a section of stirrup leather before threading it, but err on the side of caution so that you don't end up with too short of a chin strap at the end. The stirrup leather in these photos is "rough side out", so it is threaded with the rough side facing towards the horse's chin.
After coming out of the second slot, loop the leather back onto itself and through the nearest elastic.
Move the marker elastic onto the buckle end of the leather, and then buckle the chin strap, using the elastic as a keeper. You can trim off any excess leather an inch or so beyond the furthest hole. If you are using a stirrup leather with roller buckles such as this one, you might consider wrapping the roller in Vetrap to dampen any jingling.