To register your design in one jurisdiction, determine where your product will be shipped to and submit all of the required information to the organization listed below. They will review your submission and return a CRN. If your product is a vessel, the CRN is stamped into the nameplate. Example CRN number 357.5 registered in Ontario.
Getting your design registered in more than one jurisdiction is a bit more difficult. The above example first registered in Ontario could then be sent simultaneously to other regions, which would also review your design, and if all goes well, would also register it. If the design 357.5 was sent to B.C. and Alberta they would send back registration numbers 357.51 and 357.52. You combine the numbers to get CRN 357.512.
The process can get more difficult. Often the jurisdictions have questions which were not covered by the first review, and additional information is required (each jurisdiction has its own rules and requirements). If changes to the drawing or calculation are required, then the changes have to be sent back to the first jurisdiction to accept, and update the CRN number, then it has to be sent out to the other jurisdictions to accept.
Further note: Just because one jurisdiction accepts a design, it can not be assumed that others will as well. It is not worthwhile looking for the "easiest" province to get a design registered in first. It is more worthwhile to get the fussiest, pickiest province to register the design first, then submit the design to other provinces who often will come back with fewer questions about the design.