From what I understand, and probably the case most of the time when people ask about general tags and where to hunt, the problem is actually with looking at the right place and the right thing.
Go here:
http://www.albertaregulations.ca/hun...ason-wmus.html
Find what area you want to hunt in and click or tap on it. For an example, I am on my phone, so I tapped on Foothills WMU Seasons highlighted on the image below:
That took me to the page where I can see open seasons for all big game in Foothills by management units. The black square indicates a draw tag is required for the particular species; no square indicates a general tag:
On the image above, you can see that to hunt mule deer in 310, 312, 334, 336, 348 you need a draw tag during the general season (what people call rifle season) November 1 - November 30, or a general tag for archery season September 1 - October 31. Whitetail deer is not on draw in any WMUs due to the lack of a black square and you can buy a tag over the counter and hunt according to the open seasons as described above.
Now pick the zone you want hunt in and see when and what you can hunt without a draw. You can ask here if you have any further questions or still not sure about your interpretation of what you see and I am sure someone will reply.