This TripAdvisor Traveller Article discusses the pros and cons of various bases in the Rockies, including Banff and Lake Louise:
Traveller Articles are written by TA members like you and me, in response to the most popular forum questions.
You can take a Brewster Connect from Calgary airport or downtown Calgary to Banff &/or Lake Louise.
The Banff Airporter goes from the airport to Banff.
Brewster Connect and Greyhound will both take you between Banff and Lake Louise; however, if you're skiing, there is a ski shuttle that will take you from Banff to Lake Louise as well. I don't know if there is one that will take skiers to Norquay and Sunshine from Lake Louise.
In the Banff townsite, Roam transit buses will take you most places within the town limits. Lake Louise is a tiny village, and has one taxi service which charges a flat rate per customer; I think it's $7 per person per trip. In summer you can walk most places in Lake Louise (except for the Fairmont Chateau Lake Louise, which is a bit far for some), but in winter that may not be as practical.