creating premium content

How can I organize modxcms to have premium content?

I mean:

Have 2 groups of users, normal and premium. And make part of the content of the sites available only to the premium users.
Something like a page that show a description of the company, but premium users can see some more paragraphs.

And... is there any mod out there that users can pay a fee to paypal to become premium?

You can use the web usergroup and document group facilities, look for some documentation here. Menu builders etc. automatically show/hide content based on the user and document details.

There is a paypal button snippet, but no ready-made system to make your normal users premium automatically on payment.

Just as an extra to what doze mentioned, if you need to assign only parts of a page to premium members, then use the Membercheck snippet (look in the repository).