How to set up Google Mail and apps for your own domain

Go to http://www.google.com/apps/intl/en/business/index.html for businesses or in our current case to http://www.google.com/apps/intl/en/group/index.html for personal
Click "Get Started"
Fill out the forms
Verify the domain by either
- putting a file under www.domain.com/file.html
- adding a meta tag to a specific file on the top root level
If you wish to enable e-mail, you have to get MX records set up usually by the hoster of your webspace. The instructions can be found on Google.