I would like to believe that in academia, the criteria for this should be similar across the world. Thus, for a professor to accept your request to supervise your PhD work, your proposed work should be aligned to his/her research/teaching interests, he/she should find your proposed work novel and interesting; and he/she should have the expertise, resources and time to supervise it, among others.

The process often entails writing a research proposal and submitting it to the identified professor via email, who would then, if interested, advise you on how to submit a formal application, which would often entail going through a selection process competing with other potential students. If the identified professor is not accessible, it is advisable to contact the help desk of the identified university to enquire about their application process. I hope you will find this helpful.