There are two options for getting started, up the Ellingwood & South Couloirs as described here, or up a low-angle groove/chimney to the left. The latter had several bail slings, and a lot of running water during our late season attempt. My partners opted not to bring axes, so that was our best option that day. Went back the next week with a different partner, better weather, and axes and crampons - I *much* preferred the standard couliors approach.
If you start via the Ellingwood Coulior, it is fairly natural to stay right for the initial 700 feet of the route, and just 3rd class it. However, our previous attempt showed us that there is plenty of good rock closer to the ridge crest which is low 5th class. Your choice.
About halfway up you come to the "inside corner" described in Ortenburger & Jackson's guidebook, a 25-30 foot step that is low 5th class (we actually 3rd classed it before we realized where we were). Above this point you want to more seriously try to stay near the ridge crest - we found about 8 X 60 meter pitches, mostly on or to the right of the ridge crest.
If you continue up the beautiful orange-gold buttress just above the inside corner, you will skip the first of the "caves" described in Ortenburger and Jackson.