I moved to Alberta from BC a couple of years ago, so I can share some of my experiences which will be common. Sounds like there's no RIV hassle, so unless there's something else about bringing a car into Canada from the US, there shouldn't be much else to worry about.
Before you can register the car, you will need a safety inspection done. This can be done at any provincially recognized mechanic, who can issue you a certificate valid for registration. They wiill check for the usual mechanical roadworthiness, and unfortunately, will also note if your front side windows have tint film. That said, with inspections being done privately, I am sure some places are more by the book than others.
For a US import, you may be required to get daytime running lights activated/installed, and I think will require the addition of a permanent sticker (on the door jamb?) stating that the odometer is in miles.
Once all that is done, you get your plate (only 1 for the rear, no front plate needed in Alberta), issued through an authorized private registry (1 or 2 year renewal). In Canada, the plates belong to the owner, not the car, so when you sell your old car and get a new one, you keep the same plates (unless you really want to pay more money for a new set).
Insurance in Alberta is private (not government run), so much like it is in New York. Canadian exceptions to this are BC, Saskatchewan and Manitoba (government run insurers) and Quebec (private for property, government insurer for liability).
Welcome to Canada! Which part of the province are you moving to?
