If memory serves....fast questions...
Was this dog born before November 26, 2005 or lived in Ontario on August 29, 2005? If not, it's a prohibited dog under the Ontario breed specific legislation.
Is the dog spayed or neutered? If not, has the owner met the requirements for showing the dog (contained in the legislation)?
Is the current owner giving the dog to you without charge?
The Dog Legislation Council of Canada has a handy summary of the Dog Owners' Liability Act provisions. It's not legal opinion, it's an attempt to explain the provisions in simpler language.
http://dlcc.sbmprodos.org/dolafact.htm
A municipality usually requires that residents license their dogs. You're talking about Hamilton, do you live in Hamilton? Have you checked whether Hamilton has its own breed specific legislation? Some communities do.
You ask about cost. Do you mean to transfer ownership of the dog? Did the previous owner have the dog licensed in Hamilton? If so, there's usually a form on the back of a license renewal for transfer of a dog, you should be able to get it all filled out by the owner, making sure it says GIFT, and take it with you to the Animal Control office to get your own license for the dog.
If you're asking about the cost of a dog license, you should call City of Hamilton or check the city's web site for particulars.
If the dog is registered with the Canadian Kennel Club, you'll want to get the registration certificate signed off by the owner and get the dog's ownership information transferred into your name with the CKC.
If you don't have an example of a form to transfer ownership, the form for ownership transfer that comes on the back of the dog's CKC registration certificate might provide a good template. If it's still there, I owned my last purebred over 15 years ago, the form might be different now.
And until the breed-specific legislation is changed by the Ontario Legislative Assembly, I wouldn't make any assumptions that would put my dog at risk. Everyone I know with a "banned" dog is still muzzling, leashing, etc. pending final disposition of the court challenge.
Hope that helps.