I believe for canada it is basically the same. You need your marriage certificate and your original ID and you start with your drivers license and health card, from there I think you can then apply for a new passport with your new name. You do not have to change your social insurance card as far as I know.
When filing your tax return, you simply input your new name on the return and check off the "married" status. You need to enter the date your marital status changed, so whatever your legal marriage date was, and then you are good to go.