Edmonton International Airport (YEG) is about 30 kilometres south of the city centre — a distance that requires either a taxi, rideshare, or the Edmonton Transit Service Route 747 express bus, which runs to Century Park LRT station. The bus is cheap but slow; the taxi or rideshare takes about 25-40 minutes depending on traffic and costs around CAD $55-70.
The airport has direct flights to major Canadian cities (Toronto, Vancouver, Calgary, Montreal) and a number of US destinations. International connections typically route through Toronto, Vancouver, or Seattle. Calgary, two hours south on the Queen Elizabeth II Highway, is the only major airport alternative — useful if you find better connections there.
By road, Edmonton sits on Highway 2, which connects south to Calgary and on to the US border, and north toward the Peace Country and eventually the Alaska Highway. The Trans-Canada connection runs east through Saskatchewan. The Greyhound network collapsed in 2018; private carriers now run the route between Calgary and Edmonton.
VIA Rail operates the Canadian, which passes through Edmonton on its route between Toronto and Vancouver, but service is infrequent (three times weekly) and the train arrives and departs at inconvenient hours. The journey from Vancouver is roughly 22 hours; from Toronto, around 60 hours. The train itself is one of the great long-distance journeys in North America; as a practical transport option it is not.