You have to be a permanent resident of Canada (Landed Immigrant) before applying for Canadian Citizenship. Requirements stipulate that you also must have lived in Canada for at least 3 years (1095 days) out of the previous 4 years before applying, though children aren’t required to meet this requirement. You are also expected to learn about the history, politics, geography and culture of the country as part of your Citizenship application and will be required to sit the Citizenship Test. If your application is processed and on successful completion of the test, you will then be required to attend an oath taking Ceremony where you will be awarded your Certificate of Citizenship by a Citizenship Judge. At this point you will be a Canadian Citizen and can apply for a Canadian passport. The government website has an excellent “frequently asked questions” section that comprehensively covers most of the questions you may have.
http://www.cic.gc.ca/english/citizenship/index.asp
If your British Passport expires whilst you are in Canada you can renew this via the UK Passport Service for the Americas and Caribbean. It is important that you include all the documents on the checklist and that your passport photos conform to the requirements listed on the page – Canadian Passport photos are a different size to the UK. Also the fee for processing your application has to be made in U.S $
If you need to talk to someone about your application there is a call centre number, though if you have a digital phone service in Canada this call centre cannot be accessed! Be prepared to call the UK to have them put you through to the call centre in the United States… all very inconvenient. However, if your application is straight forward you should be able to apply via post and have your application processed and receive your new passport within around 4 weeks.
Further details can be found at www.ukincanada.fco.gov.uk