I recently brought my 11 years old to Vancouver and the following was my experience:
1) Check this website with regards to the Canadian importing requirement: http://www.inspection.gc.ca/english/anima/imp/petani/petanie.shtml
2) Check the relevant website of the home country for exporting the animal
3) Check possible land, sea and air transportation for the animal. As I am from China, the most economically way is by personally traveling the animal by air. Using a commercial transportation company will cost me ten times more.
4) Check with airlines whether the pet animal can be accepted to fly.
5) After knowing what document is required in step 1, go to your vet to gather those document.
6) Buy a suitable crate from pet shops, internet or other sources.
7) If you think your dog would be stressed and anxious in taking a long flight, try "DAP natural spray". You can also try "Bach's pet rescue remedy".
8 ) Talk to the airline, buy yourself a plane ticket and inform them that you would travel with your pet dog.
9) At date of departure, make sure you put some ice cubes and pet food in the feeding tray.
10) When you and your pet arrives at the airport, be sure to declare it at the customs. You will be asked to go to the agriculture department after collecting your pet and other checked luggage. At the agri counter, you will be asked to provide the vaccination and health document of your pet and questions like number of years you owned it. After the officer examine the pet, you would be directed to pay the examine fee (CAD30 + tax) at the nearby cashier.