Season for non-draw tags (and most draws) runs from august 25 to october 31 north of the trans-canada, it starts september 1st, and closes october 31st south of the trans-can.
Sheep hunting 101: (keeping in mind that I'm pretty much the opposite of an expert. I've only been hunting them for 4 years , but I mainly taught myself, so I can maybe help with how to get started.)
Find an open non-draw zone and check previous success rates. I think the last study of hunter success available on the web is from 2001. This comes in handy for finding out averages of sheep density in your preffered zones; keep in mind, however, that higher success rates could easily be a matter of higher hunting pressure, rather than higher sheep density.
Now you've got some zones you'd like to try narrowed down, go buy topos for those zones. Google earth is handy, but for id-ing good sheep country, you need the maps. You can find good sheep country from a topo by focussing on wide, (relatively) gently sloped ridges above treeline and hanging valleys. These will generally be high alpine meadows, and that provides sheep with their food. These high meadows, however, need escape cover nearby, or they will likely be unused. So you need to make sure that the higher, more gently sloped ridges are contiguous with steeper, nastier country with scree slides or loose rock. This is sheep escape cover.
What you're looking for will look something like this:
"A" is grazing habitat, "B" is an example of escape cover. Notice also that the hanging valley drops down slightly below tree line - the old rams often use trees as cover as well.
Finding small bits of topography that have both those elements probably won't work: you need large, contiguous sections of good sheep habitat for there to be enough sheep there to be worth hunting.
Once you've found some decent looking country on the maps, you need to scout it out; sheep often use historical ranges, so some likely looking sheep country won't have sheep. Furthermore, sheep segregate themselves by ### except during the rut in November, when you can't hunt. Often, Rams and Ewes will use completely different mountains, and use the same different mountains year after year, and if you walk out on opening day and find yourself surrounded by Ewes, you're screwed. So try to find rams - it's best if you find a shooter before the season opens, but if you find groups of younger rams, that may be good enough - other rams in the area will likely use the same range, and the older ones are good at not being seen.
I don't even look for sheep country closer than 15 hikable clicks from a road, or that can be accessed by quad. Too many hunters means no sheep, but that's just me.
Now for hunting, it goes like this. Haul in a 50 pound pack to your camp just below treeline. Get up at 4 in the morning to climb to the top of a mountain. Sit there with binoculars freezing your ass off looking around, maybe getting snowed on, maybe dying of heat. Do that all day. Do that all the next day. Try to do that the next day, but a system rolls in with low cloud reducing visibility to zero so you can't hunt and you sit in camp trying not to kill your partner or yourself. Do that the next day
Haul your camp another 10 clicks and do more glassing. Continue until succesful or you decide never to hunt sheep again.
Or some guys road hunt - I'd rather go shopping.
Shots can be long or short. Be ready for either. Get great optics, great boots, great backpacking gear. Be in great shape.
Geez, that got more involved than I thought I would.
Have fun.