By car, Jasper is about four hours from Edmonton to the north, and four to five hours from Banff and Calgary to the south via the Icefields Parkway (Highway 93). The Parkway is one of the most scenic roads in Canada and the obvious approach from the south; allow extra time for stopping, because you will stop.
VIA Rail's Canadian — the Toronto to Vancouver train — stops at Jasper, making it the rare Rocky Mountain destination accessible by rail. The journey from Vancouver is about 17 hours; from Edmonton, about 6 hours. Reservations are required and the train runs three times weekly. Brewster/Pursuit operates scheduled bus services between Calgary, Banff, and Jasper, timed for connections with the train at some stops.
There is no commercial air service to Jasper itself. The nearest airports are Edmonton International (about 3.5 hours) and Calgary International (about 4.5 hours).