It depends on the year, and the coin! Overall, though, the Mint sets to work on choosing a design for one side of the coin, with the Queen or King of Canada's visage on the reverse side, updated every 20 years, I believe.

You can read about the individual pieces here. Some years, such as the centennial (1967), they bring out special designs. Others commemorate particular bits of Canadian culture, like the Bluenose on the ten-cent piece.

The loonie (one-dollar coin) is an interesting case; the original design was supposed to be the voyageurs that were on the old silver-dollar coins. However, when the Mint shipped the dies for the design, they were lost (or possibly stolen) in transit. The government launched an investigation, and had a new design commissioned, the Robert-Ralph Carmichael design of the loon, which led to its common name of "loonie" (and subsequent naming of the two-dollar coin as "toonie").

If you want to learn more, you can explore the Mint's site, or take a tour of the production factory in Winnipeg, where they tell you a lot about the coins!