if the car is over 15 years you get exemption from the RIV (no need to register and pay the $195+tax) otherwise you pay duties (if it's not from the NAFTA region) and taxes
Now if the car is already here with a legal Quebec plate, then it's a straight purchase, if it's from a visitor/work/study permit holder and it's paid in full (meaning the owner has the title) then you'll have to go to the US side and leave the title there for 72 hours so they can run the plate and make sure it's not stolen etc. Once that's cleared US export will stamp it and then it will be ready to be imported.
On the canadian side you have to declare the vehicle as an import and they'll do the form1 and there you pay federal and duty, after that you go home and register the vehicle on riv.ca, get it inspected and pay the provincial at the SAAQ