In Canada, once you've chosen a form of business, such as a sole proprietorship, you register your business by going through the process of registering your business with the appropriate provincial authority.
Want to register a business in Ontario? You need to register your business with the Companies Branch of the Ministry of Consumer and Business Services. If you are starting a business in Nova Scotia, you need to register your business with the Nova Scotia Registry Of Joint Stock Companies. If you are starting a business in BC, you need to register your business with the Corporate Registry. In all cases, the first step is to choose and register a business name, a process that often requires a name search. After that, it's a matter of filling out the appropriate forms (and paying the appropriate fees) to register your business.
You will find articles giving detailed instructions on how to register your business in Ontario and other provinces in my Business Registration library. In many cases, you can register your business online or over the telephone.
Note that you do not have a choice as to whether or not to register your business. Business registration is a legal requirement. (Some sole proprietorships are the exception; see Do I Have to Register my Business Name?)