Because there's no legal document involved in common-law relationship, you do not need to do anything other than moving away from eachother.
Not exactly the case. Common law relationships carry similar rights to being married in Canada. If you have, or are in the process of sponsoring someone for a PR under common law relationship, you have to sign a statutory declaration of common law and have it notarized, in effect a legal document. You need a separation agreement to show the relationship has ended.
Terminating an Adult Interdependent Partnership
An adult interdependent partnership ends when any of the following happen:
•The partners sign a written agreement stating that they intend to live separate and apart, without the possibility of getting back together (‘reconciliation’).
•The partners live separate and apart for more than one year or both partners intend that the adult interdependent relationship end.
•The partners marry each other or one of them marries or enters into an adult interdependent relationship with a third party.
Source: http://www.slsedmonton.com/family/common-law-relationships/
You do not have to move away from each other. Many separated couples actually maintain residence in the same house, but In separate rooms (i.e. room mates). If you have children, expect the process to be similar to a divorce.