The most popular route on the peak is the Sulphide Glacier. The Fisher Chimneys and the North Face are also both popular routes that are among the best of their type in the range.
The Price Glacier route is listed in the 50 Classic Climbs book (Steck and Roper), but has fallen out of favor in recent years due to a dramatic change in the nature of the glaciers on the route. Once a classic ice face, the Price is now a jumbled mess with little aesthetic value to the climbing.
The view from the summit of Shuksan is one of the best in the range. Sitting at the heart of the North Cascades, views of Mount Baker, the Pickett Range, and north to the Canadian Border peaks are completely unobstructed.
Although the route is doable in one very long day for experienced and fit parties, most opt to go for a 2-3 day climb so that they might enjoy the setting on the way to and from the climb. There are great camping spots at the toe of the Sulphide glacier and at several spots along the route to the summit pyramid. The Sulphide is a gentle glacier, but not without crevasses. There have been numerous solo climber crevasse falls in the area.
AAI climb's Mount Shuksan as part of their Classic Guided Climbs in the Pacific Northwest Program and also on Part 1 of their Alpine Mountaineering and Technical Leadership series.