By car
Alberta is quite large, as are most Canadian provinces. A rough comparison is that the island of Great Britain can fit into Alberta more than six times over. Also noteworthy is that most Albertan cities, and especially Calgary have historically grown horizontally rather than vertically and are thus really big. Car travel is essential unless you plan on staying within Edmonton or Calgary where you can walk, bus, transit. However most towns and cities in rural Alberta are more than accesible by Greyhound Bus.
Driving regulations are the same as in most of Canada. Turning right far right lane into far right lane on a red light is allowed. It goes without saying that drunk driving is taken very seriously, but is disproportionally seen in rural areas--take care when driving there at night. Wildlife is another major concern. When driving on the highways, maintain a reasonable speed and look for sudden movements on the side. The most common animal hit is the deer, which is usually not fatal for the car. But running into an elk or moose could possibly be so. Elk and moose are very dark coloured so keep a close eye out for them. If you see animals on the side of the road it is common to want to slow down. Do so in a safe manner and don't needlessly impede traffic. Don't get out of your car to see the animals.
The AMA Alberta Motor Association is a good source of specific information and offers the most widely used driving courses. Both Calgary and Edmonton offer traffic radio stations - government funded radio that only reports accidents, construction and weather. Watch for signs featuring the frequency in these cities.
Do not heed any warning about Albertan drivers being the most aggressive drivers in Canada - a common myth. They are not more so than Toronto and certainly are nothing compared with Southern Europe. High speeds and lane changes without signaling are generally the worst it gets.
By Rail
VIA Rail is the only passenger rail service into Alberta, and it goes into Edmonton from Vancouver, British Columbia and Saskatoon, Saskatchewan. There is no passenger rail service into Calgary.
By bus
Greyhound Canada offers service between almost all centres, large and small. Be aware that Greyhound does the so-called "milk runs" stopping at almost every location, usually to drop off or pickup passengers and cargo. There are other bus lines offering service between major centres, such as Red Arrow between Edmonton, Calgary, Fort McMurray, Jasper and Banff.