I changed some of the files for the cart of VirtueMart in order to display only the productlist on the first step. I've done this directly inside the components\com_virtuemart\views\cart\templ
-folder.
But now I've updated VirtueMart and all the design-changes are lost.
Where do I have to save my changes without having to upload them again after every update?
When you want to change the design of an extension, you should always do it via a template override. This ensures that when the extension is updated, your changes are not lost. Due to you editing the core files for VirtueMart, the update replaced them.
See the link below on how to do template overrides. They are very easy ;)
http://docs.joomla.org/How_to_override_the_output_from_the_Joomla!_core
Hope this helps.