Read the information here closely ...
Conversion between U.S. and Canadian Pilot Licences - Transport Canada
The medical requirements are somewhat similar to FAA. You are not issued the medical by the AME; it's sent to you by TC. You start the process by getting a medical.
The license verification took a little over a month. I sent them copies of my certificates, but I don't know if this sped the process up.
The exams are done at certain TC offices. Read through the link carefully. It's all there.