On foot
Downtown Calgary is a compact area which is easily accessible on foot. The pathway system, Eau Claire Market area and Stephen Avenue Mall 8th Avenue are the primary walking destinations of downtown workers in the warmer months. In the wintertime, everyone navigates their way around the downtown core via the Plus 15 system (http://www.calgary.ca/por...), so called because the enclosed walkways joining buildings are approximately 15 feet above ground.
By car
It is easy to be confused by Calgary's quadrant address system at first, but it is very logical, and, well, systematic.
Streets run north-south and avenues run east-west. Centre St divides the city into east and west, and Centre Ave and parts of the Bow River divide the city into north and south. Together these split the city into NE, NW, SE, and SW: the four quadrants. Thus any time you get an address on a numbered street, you MUST get whether it was NE, NW, SE, or SW. Street and avenue numbers--and thus addresses--increase as you move away from Centre St or Ave.
Many of Calgary's roads are numbered, but this is less common in the newer developments. Important roads are usually called "trails," but there are many exceptions. Note that newly-built neighbourhoods may not yet appear on maps, whether they be paper or GPS. If you are travelling to these places, it may be a good idea to ask for directions beforehand.
In general the city's driving situation is a result of rapid, unanticipated growth, so prepare for the roads being grossly inadequate and gridlocked during rush hour. Also watch for lane reversal rules during these peak times on weekdays 6:30 am-8:30am and 3:30pm-6:30pm when going in and out of downtown on some larger streets. This increases the traffic flow in one direction by "borrowing" a lane normally going the other way.
Keep in mind that driving in winter is very different from driving in other seasons. Major roads are plowed, salted, and sanded, but often smaller residential streets are not at all. Note that as of fall 2011 the city has instituted Snow Route parking bans. This means after a heavy snowfall certain priority routes in the city - marked as snow removal routes with street signs - become no parking zones for 72 hours; this includes some residential streets, so bear this in mind if you're visiting family and parked on the street during the winter.
As confounding as driving in Calgary may be driving is still the best way to explore and see the city.
By bike
With approximately 635 km of pathways and 260 km of on-street bikeways within its boundaries, The City of Calgary boasts the most extensive urban pathway and bikeway network in North America. Pathway maps are available online (http://www.calgary.ca/por...) or at Calgary Co-op (http://www.calgarycoop.com) stores. Downtown, there are many pathways along the rivers and park areas. Though Calgary can be thought of as a safe city, use common sense when biking at dusk and at night. This is particularly true on the east side of downtown along the river close to the neighborhood of East Side Village, which is a rougher end of town.
Calgary has a good network of off-street bike paths, although motorists are sometimes less-than-courteous. Weather is unpredictable, and snowy cycling conditions may occur anytime from September to May. Bike racks are fairly common, especially in shopping areas. Be sure to use the bike racks provided, or another solid object to lock you bike to; as simply locking your back wheel will not provide sufficient security. Calgary Transit has bike racks at C-Train stations and allows bikes on the C-Trains during off-peak hours at no additional fee. Some bike routes also have buses equipped to accommodate bicycles with racks on the front (http://www.calgary.ca/por...). Cyclists must remember that they must obey the same rules of the road as other vehicles (http://www.calgary.ca/por...). All cyclists under the age of 18 are required to wear a helmet, and all cyclists must have an working bell on their bike.
Each major body of water in the city bow river, elbow river, Glenmore reservoir, etc will have both city parks and thus city bike trails passing through. These bike paths are heavily used during the morning rush hour to work, but can provide hours of scenic peddling. A scenic route starts in downtown and head along the "bow river pathway" as it heads south to Fishcreek provincial park. Here, leave the banks of the bow river and cycle though Fishcreek Park park along the main cycle path path until you reach the Glenmore reservoir a good place for lunch. At the reservoir, as the bike path crosses the Dam, leave the "bow river pathway" for the "Elbow river pathway" This highly scenic path will take you back to downtown. Cycle time : 4 -6 hours with lunch.
Another major pathway extends north up Nose Creek valley just east of the zoo, including two overpasses to cross Deerfoot Trail busy freeway. While there is a pathway that leads to the airport, connecting to it requires crossing an industrial area, which is not recommended for novice cyclists. Cyclists are not permitted on Stephen Avenue Mall or Deerfoot Trail.