is there a quick way to export the complete data from my database?
The short answer is "Yes" but it's not as useful as you might think.

First - consider a contact with 10 donations, 5 events attended, 3 memberships, etc.  If you exported this all in one table, it would be hundreds of columns, with data flattened to the point of uselessness.  On the other hand, if you export contacts in one table, donations in another, etc., it's quite hard to make good sense of what you're looking at since it lacks context.

My recommendation is to search for all contacts (going to Search menu >> Find Contacts and press Search without specifying any criteria).  Then from search results, select the All Contacts  radio button, and Export Contacts from the Search Actions drop-down.  Export All Primary Fields.

This is a) still information overload, b) doesn't contain quite a lot of database information, but will serve as a helpful starting place to familiarize yourself.