It's worth stopping at in the park warden's desk in the Icefield Center before your climb. They maintain a climber's log, which can provide useful beta on recent route conditions. To keep the good karma flowing, stop in on your way out and put your own entry in as well.
ApproachFrom the Icefields Center, take the Snocoach road about a kilometer to a parking area on the left just past a small wooden bridge. The road is gated during work hours, but you can just tailgate behind a bus, or drive around the gate if your car fits--they are used to accommodating climbers.
From the parking area, follow the climber's trail up the moraine to the Little Athabasca Glacier. Hike up the glacier towards the Silverhorn, staying generally left on the glacier to avoid crevasses and the objective hazard posed by seracs to the west. Just below the Silverhorn, head up and left into the cirque beneath the North Face. The west side of this cirque is threatened by seracs that have been known to release monster ice avalanches, so give them a wide berth, and don't dawdle beneath them.
Up to the Silverhorn the approach follows the North Glacier route. This is a trade route, and in summer there should be a well-beaten path. I'd suggest following it, as the guides who travel it nearly every day do a good job of route setting to avoid the majority of crevasses.
Cross the bergschrund where convenient, and head up the face for approximately five pitches of 45-degree ice (or snow, depending on season). You're aiming for a narrow chute in the center of the rock band above. This will become more obvious as you ascend. A short, steep crux is followed by two more pitches in the snow/ice gully above. You top out more or less on the summit. The crux is protected by three fixed pins. There is a fixed pin belay anchor about 20 meters higher in a notch on the right-hand side of the gully.
About 100 feet left of the standard exit through the rock band is another potential exit involving a short, steep chimney leading to lower angle rock. It is also possible to traverse from the base of this chimney back right across ledges to just above the crux on the standard exit, though in the "right" conditions this is quite a bit more tenuous and difficult than the normal route. Fixed pins on the traverse attest to the fact that more than one party has done this. Not recommended.