We had the trial version of Confluence, bought a license for our own server and how could we transfer all data from the trial version database to our own database on our SQL-server?
You have not explicitly said which database you have in your trial version. A trial could use any database you choose, but a lot of us will use the "embedded" one which requires no set up (but is utterly unsuitable for long-term or production use)
If you chose to use a SQL-Server for the trial, then you can just dump and restore the existing database.
If, as I guess you probably did, use the "embedded" database (or any other really), you'll want to do a migration. See https://confluence.atlassian.com/doc/migrating-to-another-database-148867.html
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