How to use user stories in Scrum

The work.on a Product Backlog is there to allow Sprint Goals to be identified and committed to in Sprint Planning. A Sprint Goal addresses and mitigates a significant risk or uncertainty in a complex challenge. Product Backlog items, such as user stories, are there to enable this conversation.

Product Backlog refinement is the art and science of making work ready for Sprint Planning. 

Enough refinement should therefore be done to ensure that the question in Sprint Planning is never: "Can we do this work?". The Developers know they can. Rather, the question is: "Should we? Should we do this work in order to achieve a good and meaningful Sprint Goal? What would that Sprint Goal be?"

So now im wondering how i should proceed as a scrum master?

As a Scrum Master, you really have nothing to do unless there is an identifiable issue with the way that the work is done and the result that is achieved. If the Scrum Team is delivering at least one usable increment of valuable work in every Sprint, then why would you want to do anything? Remember the Scrum Master responsibilities described in the Scrum Guide (https://scrumguides.org/) have nothing to do with managing processes. 

There is no "right way" to use User Stories in the Scrum framework. The Scrum Guide does not mention them.  The Scrum framework uses Product Backlog Items that describe the changes that need to be made to the Product. They can be in whatever format that the Scrum Team feels works best for them. 

What your question is about is a process that is different from one company to another.  Again, Scrum is a framework and not a process. So processes can, and usually will, differ from one company to another. In fact it can differ from one team to another. 

...already see huge differences how they use scrum.

This is something that you can expect as you get more experience. Since Scrum is a framework, it can be used with a variety of processes and can appear to be different.  However, if the organization is truly using the Scrum framework, there should be specific underlying practices, not processes, that will exist as they are described in the Scrum Guide. 

Your process question is related to refinement of items in the Product Backlog so that they become ready for inclusion in a Sprint Backlog.  This is the only section of the Scrum Guide that comes close to defining the act of refinement.

Product Backlog items that can be Done by the Scrum Team within one Sprint are deemed ready for selection in a Sprint Planning event. They usually acquire this degree of transparency after refining activities. Product Backlog refinement is the act of breaking down and further defining Product Backlog items into smaller more precise items. This is an ongoing activity to add details, such as a description, order, and size. Attributes often vary with the domain of work.

As you can see it is a high level description and does not provide any specific actions or process. The "right process" is whatever works best for the individual Scrum Team within the organization for which the work is being done.