They are usually presented in list or scenario format.
They can be written in natural language: what matters is that they clearly reflect the intent behind each criterion, not that they follow a formal syntax.
Although the Product Owner may have prepared them in advance, they are finalized as a team during refinement or Sprint Planning. The conversation this process generates is as valuable as the written result.
It is the Product Owner's responsibility to ensure that the criteria cover all the aspects the team needs to estimate and develop the story properly.
In the Sprint Review, the Product Owner checks whether each story meets the defined criteria in order to accept it or send it back.
