This is a big mountain day - lots of vertical in a short distance, an ascent with a definite crux, and stunning views. Mt. Stephen was the first mountain over 10,000 feet to be climbed in Canada. The southwest ridge was the route of first ascent and is the regular route today. Competent climbers can solo the route, but it is wise to take an ice axe, a rope, and a small rock rack.
It is no longer possible to be casual about an ascent of this peak. Parks Canada's concern over theft of fossils from the Mt. Stephen fossil beds necessitates that you obtain a permit before you can cross Stephen Creek. You'll have to get the permit the day before because you'll want to start on the trail early. Don't skip the permit. The trail is monitored with electronic gizmos that will record your presence. The infraction for which you will be cited is "entering a closed area." It carries a mandatory court appearance, probably in Golden, BC.
The Canadian Pacific Raiwlay cut the Mount Stephen trail in 1894 to make easier at attempt on Mt. Stephen that year by members of the Appalachian Mountain Club. The trail is a grunt from its beginning (51:23.7-116:29.0) to its end, about 2.5 km later, at the lower fossil bed (51:23.3-116:27.7). A beaten path continues, contouring on steep sideslopes and through rotten shale cliffs onto the broad shale slopes at the base of the southwest ridge (51:23.3-116:27.2). The way is obvious, at least initially. At about the 9300 foot contour, you have to start paying attention to the route, which takes any steep terrain by moving east or south - never west! You will negotitate a system of balconies and ledges that defies precise description. If you are using your hands for climbing, you are off route. At about the 10,000 foot contour, options diminish. A steep, often icy gully drops away to the south, and a wall that comprises the crest of the southwest ridge looms to the north. Step around the top of the gully onto a ledge at the base of a short cliff. The rock is good with good holds. This section is 5.2. Above this many people take to the ridgecrest, which is a knife edge with almost 2000 m of exposure to the north. But it is possible to traverse beneath the ridgecrest until beneath the summit, then climb up over rotten ground with a few short cliff steps - one or two lower fifth class moves - to gain the summit (51:23.9-116:25.9).
Many people think that they can add variation to the descent - there must be a faster way down all that scree and rubble. Generally speaking, unless you fall down the gully mentioned above (it's been done), there isn't. Take every bone-jarring step with patience and caress your knee cartliage at day's end.