North America is the best continent to control when playing Risk. If possible, place as many armies as possible in your North American territories, and then make conquering it your first priority. Once it is conquered, focus your attention on defense. North America is only the best continent if there is no risk of losing your core territories. Put a sufficient amount of armies in Greenland, Central America, and Alaska. If you've already conquer countries bordering these, continue to slowly expand outward, defending the countries as you go.
After properly establishing good defense for North America, strategy comes into play. North America's unique tactical position makes it great for the strategic Risk player. Because of it's three strangleholds, it makes it easy to protect, and being isolated makes it difficult to attack. Depending on turns and other variables, I suggest making an attack on Iceland ASAP. More than likely, whoever is in control of most of Europe, has already received multiple attacks from other players due to it's 5 continent points and impressive strategic position. This makes it easy for you to roll right through will ease, keeping in mind not to spread yourself thin. Again, the most important part to the success of the North America strategy is its defense. Alaska is another good place to attack from, but again all is relative to the defense in Kamchatka. If you have to make a desicion, play conservatively and only fight on one front - in this case, Europe.