Edmonton  is the capital of Canadian province of Alberta. With an area of over 600 square kilometers, prepare yourself for some walking if can't get a lift out of the city. It is preferable to avoid hitching out of Edmonton during the winter months as temperatures can fall below -30° for many days at a time. This can be dangerous if you are not prepared for it. One would hope that drivers would be more willing to stop for a hitchhiker in the bitter cold, but don't assume this to be the case. Hitching outside of the city limits is perfectly legal, as far as I know. Hitching inside the city will save you some walking and you most likely won't have any problems with the police if you are not causing any danger. An Edmonton Transit System bus fare pays for a complete journey, including transfers for up to 90 minutes which should be enough to cross the whole city.
Highway #2 heads south as Calgary Trail (103/104th street), splitting Edmonton in half. A good spot to start hitching is just south of Ellerslie Road. Bus 49 from Heritage terminal will take you to Ellerslie road. From here it is approximately a 3 hour drive to Calgary.
West toward Jasper
Highway #16 crosses Edmonton's north end as the Yellowhead Trail. Heading west it is 4 hours to Jasper National Park. Bus 126 from Westmount terminal will take you to 184 st. Walk north from there a few hundred meters to the Yellowhead. It may be a bit tricky to hitch there but there is an on-ramp.
Recent construction in Edmonton of the Anthony Henday ring road makes hitching west difficult. The interchange between Anthony Henday Drive and Hwy 16 is constantly changing, making this area confusing for local motorists and hitchikers alike.
One location that provides a good on-ramp would be the overpass where 16A meets Hwy 16. There should be less local traffic and more long-distance traffic. This location is however 30 kilometers from the outskirts of Edmonton.
Your best bet is probably to try hitchhiking from the truck stop on the south side of the junction between Hwy 60 (Devonian Way) and Hwy 16, although it is still 5-6 km from the outskirts of the city. It also has a good on-ramp.
East toward Saskatchewan
The best spot for going east is right beside the Rundle Golf Club. Type this into google earth, (edmonton, rundle golf club) and you'll see the ramp just north of it. Take the number 8? Or whatever bus it is that gets you to Abbotsfield station and walk back 100 meters across the street, by the lights and you'll see the sign that says 'Victoria Trail and Trans Canada', take the trans Canada.
There is also a truck stop just outside the city at the junction of Broadmoor Blvd. and Hwy 16, although it is in Sherwood Park and might not be very accessible.
North towards British Columbia, Yukon
If you are heading towards Fort McMurray, Highway #28 cuts up the middle of Edmonton's north end as 97th street. Bus 163 can be taken from Northgate terminal up to 176th ave which is close to the northern city limits.
If you are heading north-west towards northern British Columbia, the Yukon and Alaska, head west as described above. About 40km after leaving Edmonton, Highway #43 turns to the north. This is what becomes the Alaska Highway (just 2500km to Alaska!).