Your auto insurance provider will send you paperwork a few weeks before the renewal date — this is generally a good time to start shopping around for rates.
That said, you don’t have to wait until your policy is close to expiring. Seeing what’s out there at any point of your contract is a good idea. Although they are subject to provincial regulatory oversight, insurance rates are not determined by the free market. Each company uses its own claims history to set rates (though provincial governments have a major hand in regulating rates; take the Financial Services Commission of Ontario, for instance), so you could very well be paying too much.
As for how long quotes are valid for, that varies company by company. However, any deadlines should be prominently displayed, and when quotes do expire, you should not have any difficulty getting a new one.