adding multiple content elements to a page? I am coming from TYPO3 and like Drupal a lot so far. Especially how easy it is to define custom content elements with the fields feature.

But what I kind of miss is this:

In TYPO3 you have pages which can be filled with content elements of various kinds (text, text with images, tables, forms,...). I like this a lot. It's versatile and harder to mess something up for the editors compared to simply having a "page" where you have a big text area you have to work in.

What the best way to achieve something similar in Drupal?

Edit:
Here are two example screenshots of the TYPO3 backend:
http://www.aemka.de/fileadmin/_migrated/pics/Backend_2_02.png
http://www.form4.de/typo3temp/pics/faa6f10095.jpg

Yes, it seems like those panels are exactly what I am looking for. Thank you! :)
It seems you are looking for https://drupal.org/project/panels. It gives you the ability to add various types of content.