From the Kootenay Park road, take the road that goes to the mine, some 60 km from Radium Hot Spring. At the mine, turn right on the small dirt road for about 1 km. Park there, then fallow the trail to the base of the mountain. The hike should take some 4 to 5 hours. Camp pass the lake, on the high "plateau".
When facing the south face of Assiniboine, climb left of the obvious pyramid. Route finding will be challenging.
Rope (60m), crampon, ice axe, some Trad protection, slings that you'll leave behind when rappelling and a HELMET. Don't forget your helmet, rocks fall all the time on this mountain!
Once you reach the lake by approaching by the valley, you'll see a high plateau. This is where you should camp in order to have a chance to reach the summit. See picture.