well it was different for me because I didn't come straight to edmonton. I moved directly into my wife's apartment in a little tiny remote town in the FAR north of alberta, on a Cree reserve. It was only during the winter I came to edmonton so I was already here in alberta.
Immigration for me was easy because I came by the family class immigration route, which takes only about 6 months. It wasn't convenient or cheap but from what i've heard it's a lot better than the skilled worker route. The actual travelling is no big deal... I came as a visitor, and got my permanant residence while I was here, then I had to cross the US border and re-enter to validate it. I spent a total of 45 minutes in the USA. Setting up alberta healthcare is simple enough, just follow the instructions on their website...
Coming from trinidad I expect you might not be prepared for the winter here... In edmonton it sometimes gets down to -30°C, and where i was to start with it hit -50°C a couple of times. Having said that, it's quite dry here so you don't feel it too badly. Lots of layers and a cheerful disposition help. I think the winter in Calgary is usually better but it can still get cold at times, and I think their weather is less predictable because they're so much closer to the mountains.
The biggest difficulty for me was crossing the road. In england we drive on the left so I always looked the wrong way. Also here when you stand by a road, cars stop to let you cross, which is very embarrassing if you were just trying to decide whether you needed to cross. Also they have jaywalking laws here which don't exist in england, so you have to cross at crossings.
Another thing I'll never quite get used to is the SIZE of Canada. Everything is further apart, and bigger. The towns are bigger, the houses are bigger, the cars are bigger, the roads are bigger... and it's perfectly normal to drive for 24 hours to get somewhere. In england, if you drive for 24 hours, you'll get wet, unless you go in circles.
As Karrie mentioned, Edmonton is highly multicultural... my landlord is from trinidad, in fact. Unfortunately there are some Canadians who see this as a bad thing, but generally I feel very safe and happy in the city.
The REALLY hard thing in either edmonton or calgary is finding a place to live. I spent months looking for an apartment which allows children, and when I finally got someone who answered the phone, they always turned out to be either not renting, or not renting to families with children. When I found an apartment I had no choice but to take it, despite the fact it's not ideal. Canadians whine about the cost of the rent in edmonton, but for a british person it's actually quite cheap. The same goes for a lot of things.... gas, for instance costs half of what it costs at home, and yet the Canadians moan about it all the time.
My overall impression is that Canada is a fantastic place to live, alberta is the place to get a job, for sure, but not a house, and most Canadians don't know how good they've got it.
If you have any specific questions, feel free to add me to msn or email me or PM me or whatever. I'm happy to help.