What are the expectations for a Ph.D. candidate in Scandinavia in particular?
In Finland, you usually start your PhD studies after your MSc studies. If you don't have an MSc yet, get it first.

Other than that, there are no unusual requirements or expectations. You just have to convince your potential supervisor that you personally are the best person in the world for this position. Hiring a PhD student is a huge investment — in the ballpark of hundreds of thousands of euros of grant money, plus numerous hours of their time to supervise the student — and you really have to convince the professor that you are worth all that.

A fairly common approach is to do your MSc studies in the same place, get to know the professors, work as a summer intern in their research groups, write a MSc thesis under their supervision, etc., and this way gradually convince them that you really are not just an excellent student but you also could become an excellent researcher.