The procedure for common-law sponsorship and spousal sponsorship GENERALLY is not any different. Most of the steps are the same.
Some of the forms have separate sections or questions for common-law partners to answer, and/or sections that are just for married people to answer. It's pretty obvious on the forms (i.e. the questions where you are asked about your marriage ceremony, for example). The main difference between a spousal sponsorship application and a common-law application might be in the proof of relationship section - as you must provide proof of having lived together for at least 1 year before applying. You should likely also include evidence that your lives are financially and legally intertwined - that you are beneficiaries on retirement accounts or insurance policies and that you have joint bank accounts. Married couples may not need to provide as much evidence of this type, as the marriage implies these kinds of legal arrangements.
I would also recommend applying outland instead of inland, unless you have a real reason to apply inland. Outland applications through the buffalo visa office are processed in much less time, and the american partner can still be in Canada with the canadian partner while the application is being processed (my common-law partner is currently in Vancouver with me on a 1-year visitor record).
Hope this helps, and if you have more specific questions, don't hesitate to ask!