Confused on who runs Canada?

Ok so Canada is really confusing as is Australia and other countries associated with the queen of england, the thing i dont seem to get here is people say that the queen has no constitutional rights over those countries and that shes just a mere culture symbol of the Anglo-Saxon world, ok fine, then you have other people saying that shes the ones that makes the laws and that no law is passed until her approval, and that new citizens have to swear loyalty to her, i mean is Canada an real country..., this is really confusing can someone please explain, i beg you