If you are looking into registering a .DE domain name for emailing purposes and not using a freemail service like gmx.de or web.de, you have a couple of options:
1. Register a domain name with your favourite registration service, and then pay the same or another company to host it (as long as they have the appropriate tools and apps. I'd go for GoDaddy.com. A .de domain with them goes for about 14€/year (.com et al go for half) and their cheapest hosting for almost 4€/month.
2. Find a free hosting service. I have had good experiences with Google Apps
. You register the domain name through them (they will do the paperwork for you with GoDaddy or someone else automatically) and they will host it for free, as long as you picked the Standard Edition. Then, you can use all their services instantly (websites, calendar, etc.) or just stick to email, which is based on the Gmail platform. This can be set up in under 5 minutes flat and all you are paying for is the yearly domain name registration fee (again aprox. 14€/year for a .de).