If you are a US citizen and commute from the US to Canada to work everyday then you do not pay Canadian taxes. Canadian income tax is on the basis of residency rather than citizenship.
However if you are a US citizen that lives in Canada either part time or full time for the purposes of employment then you are considered a resident of Canada. Then you must file two returns each year: a Canadian return because you live there full or part time, and a U.S. return because you are a U.S. citizen. Fortunately, this does not necessarily mean you'll have to pay taxes to both countries but depending on your income you may be required to pay taxes in both countries.
You may be able to exclude up to $85,700 from income for US tax purposes by completing Form 2555 and attaching it to your return. Form 2555 is a special form excluding foreign earned income from taxation in the United States. To claim this exclusion you must be a bona fide resident of Canada or must have been living in Canada as a part-time
resident for at least 330 days out of the last 12 months.
You are also allowed to claim a foreign tax credit on your U.S. return for taxes you are required to pay to Canada. To claim the credit, you must complete Form 1116 and attach it to your U.S. return. Alternatively, you can claim the Canadian taxes you paid as an itemized deduction. Both the deduction and credit are limited to foreign income that is subject to U.S. tax, so neither can be claimed for income excluded on Form 2555.
If you live outside the U.S. you have an automatic extension of two months to file your U.S. tax return. In other words, your U.S. return is due on June 15 each year, rather than April 15. This provides time for you to complete your Canadian return and determine your Canadian tax liability. This is needed in case you have to claim the foreign tax credit on your U.S. return. Note that while you have until June 15 to file your US tax return if you live in Canada, the IRS will begin assessing interest on any unpaid balances on April 15th.