As a Landed Immigrant of Canada, you are liable to pay taxes to CCRA on your world wide income. You will use form T1to file your Canadain Federal Return and the appropriate provincial form to file your provincial returns.
Here is the link to CCRA to download the forms:
http://www.ccra-adrc.gc.ca/menu-e.html
Technically if you are not living in Canada, and do not have any ties to Canada (bank account, credit cards, health card, real estate, family) then you do not have to file your Canadian Returns. Keep in mind that this could/will jepordize your Application for Canadian citizenship. As of now, I don't think you will have to prove that you have paid Canadian taxes when you file your Citizenship application.
If you decide to file your Canadian Taxes here is the calculation to determine your Canadian Income.
US GROSS INCOME+Dividents+Intrest Income * $1.4014 = YOUR CANADIAN INCOME
Why $1.4014? This is what CCRA uses. CCRA uses the Annual Average exchange rates published by Bank of Canada.
http://www.bank-banque-canada.ca/pdf/nraa03.pdf.
You basically Calculate your Canadian Taxes and deduct the following: (the below info should be used from your 1040 and the appropriate state/city returns you filed. You cannot use the witheld amounts from your W2. You will have to use the amount you owed on 1040)
Federal Income Tax Paid+State Income Tax Paid+SSA and Medicare Taxes * 1.4014 = Foreign Tax Credits!!
Here is the link to the Tax Treaty agreement which states you can deduct your paid Social Security Taxes (look up Article XXIV)
http://www.fin.gc.ca/treaties/USA_e.html
Also keep in mind that once you take the Foreign Tax credit on your Federal Return, you cannot take this amount again on your Provincial Return.
Good Luck!!