Your situation is strange, but not too rare. Find an accountant familiar with these types of setups, and ask him for advice/have him prepare your taxes, since the devil is in the details, and generalities below may not apply, or apply differently to you (he'll be able to answer questions along the lines of "which country should I pay my taxes to first?", for example).
That said, generally speaking:
Canada and the US have income tax treaties in place. You should, once all is said and done, find yourself mostly paying taxes in just one country, and paying off some small differences in the other.
Most likely you have taxes deducted on your US salary by your employer. On your Canadian return, you'll be able to claim the vast majority, but not all, taxes paid in the US as deductible. Canadian taxes are generally higher than in the states, and you will find yourself responsible for both the difference in taxes, and for (a small portion) of taxes not covered by treaties.
It may not be applicable to you, though - you may find that you're required to pay most of your income taxes in Canada, and not in the states. It may be that almost all of your US taxes will be refunded to you, and you'll find yourself paying full Canadian income tax.