If you're not catholic or Christian, you can hire an officiant to marry you guys, refer to the following site, they charged us $280 (all inclusive) a year ago. http://www.ottawaweddings.ca/
The ceremony can be done anywhere, not necessarily church: you can choose your living room (you two, officiant + 2 witnesses), or at a backyard garden, or rent some public park. It'll take 30 minutes or so and then you sign all the paper, (including a temporary marriage certificate) submit all the signed documents to Ontario Minister of Consumer and Business Services - Office of Registrar General, it'll take several weeks to receive your final official marriage certificate.
OR
You can choose to get married in Quebec, City Hull, Promade du Portage, it costs about $273 + tax and application fees (this figure I can't remember that well)