If you're a Canadian citizen planning on doing flight training in the US, the following outlines the process you're going to have to go through in order to get your PPL:
1. Contact the flight school from which you'd like to receive instruction from in advance (this will be important later on in the process)
2. Go through TSA's ASFT (or some other acronym I can't recall for Alien Student Flight Training) approbation/inquiry process. This can take a while to receive clearance from, especially if you do not have a designated facility for taking your fingerprints. TSA will notify and double check with the flight school you listed in the paperwork).
3. Once cleared by TSA, you must begin flight training in 180 days of your approbation date and finish in under a year. If not, you will be required to resubmit an application (mostly meaning paying the fees again!)
4. You will need a US Medical Certificate before you can fly solo during training.
5. Once you receive your US PPL, you can apply to TC for a transition to a Canadian PPL. I remind you that the following steps are only valid for PPLs as any higher licenses must follow are more stringent process.
6. TC will do a background check with the FAA Airmen Certification Branch to attest that you do hold a valid US PPL.
7. After being cleared by TC, you must go through the transition process, fill out the Canadian paperwork and get a Canadian Medical as well.
I'm sorry if I missed any steps but this is as good as I can remember. I do not mean to rag on US-Canadian bureaucracy but, IMO, you would be better off simply getting a Canadian PPL if you do not plan to fly N-numbered aircraft in Canada. Believe me, I'm writing this even though I am fully aware of how much more tedious it is to get through the bloody licensing process in Canada compared to the US...!