Here you have the official rules, by the International Federation of Padel:

Rules

It's a long pdf file with 33 pages. Though it may seem to be a lot, it's too technical on the field, so there should be another straight-away version coming soon.

The Padel Association of Canada has uploaded a shortened version of the rules.

Check their site: Canada
You'll see the "basic rules" highlighted in red in the middle of the website.