From the upper saddle (13,160'), rope up and belay from a large boulder near the north face. Continue around towards the north face to reach the "belly crawl", an obvious and well named feature. It is a ledge not more than 18' wide with an overhang above. The exposure here is very exciting. Continue traversing around the ledge about 15' to the double chimney (P1), the technical crux of the climb, about 5.4.
Directly above this is the Owen Chimney (P2) which angles up to the right. The route from here goes north east to a third, very large chimney called Sargent's Chimney (P3). From the top of Sarg's, continue up and to the left. Pay careful attention to your assent path from Sarg's, you will need to find it on the down climb and it isn't obvious!
For the descent, downclimb Sarg's Chimney and then make your way to the left to a 120' rappel that drops you directly onto the upper saddle.
The route finding can be difficult, particularly on descent given the whole mountain shows signs of traffic. There are many variations to the route depending on conditions.
Buy the guidebook: "A Climber's Guide to the Teton Range" by Ortenburger & Jackson. It is perhaps the greatest guidebook ever written.
Location
Getting up to the upper saddle from the lower saddle is a climb all unto itself. The guidebook provides an excellent description.
Protection
A small alpine rack is fine provided you are familiar with using natural features for belays and 5.4 climbing is easy for you.
I did this without roping up a number of years back. I was in a Colorado 14er mode and thought I would skip the hassle. Not smart.
The climb is quite easy but there is a stretch just after the "belly roll" with a 5.4 move and about 2000 feet of exposure. I believe you would land somewhere near the bottom of the Black Ice Couloir if you goofed up.
You need a rope anyway because you have to rap down - or down climb the exposed 5.4 move, which you wouldn't want to do.
So take a light rack and enjoy yourself. Beautiful climb!
When dry, this route is not difficult although you can still get off-route. However, it faces NW and after a snow or hail storm it can take many days (if not weeks) to dry off. There was one summer when it kept getting snowed on, and the route was in "winter condition" all summer! The guides had a really bad season that summer. Even on a good year by September it usually receives a dusting of snow.
From above this route is difficult to find and it appears improbable. I've downclimbed it once unroped when dry, but this was with a person who had gone up it the week before. This is a quick way to bypass the crowded raps, but I wouldn't recommend it.