Hi Johannes and welcome to Umbraco.
You will need to convert the aspx pages into HTML templates, you can use inherent so you don't have to keep writing out the same HTML.
Along with this you will need to create document types to allow you to use your data.
For example if you have a contact form on an ASPX page you will need to put the contact form functionality into a usercontrol (.ascx) but the rest will be handled by the html in your template.
I am probably not explaining this too well at the minute, but I would recommend my website starter wizard, it will install an entire website into an empty umbraco installation.
From there you can take a look around and see how things relate to one another and try to modify things for yourself to learn umbraco, that's the best way in my opinion.
To install my wizard once you have installed a new version of umbraco, login into umbraco goto the Developers section.
Right Click Macros
Select Import Package
Select Open the Repository
Select Website Packages
Select Creative Web Site Package
And follow the steps from there.
I hope that helps you, if not come back and ask more questions :)
Warren
Warren Buckley an Umbraco MVP 08-09 & level 1 certified developer