German sign language is called Deutsche Gebardensprache and, like American Sign Language, German sign language is a way of communicating without using speech that has been evolving for many years in the German deaf community. The deaf community uses Deutsche Gebardensprache to communicate with each other and sing songs. Non-deaf Germans also learn sign language so they can communicate with those who cannot hear.
Master the German language in spoken form. Just like American Sign Language, German sign language really requires you to know how to speak German like a native speaker.
Find a German class that studies or gives an introduction to German sign language. This can be difficult because it isn't taught widely. However, at a very large university with a large and extensive German-language program, there may be a class or two offered on German sign language.
Enroll in a German university. There are several German-immersion schools in the United States, but the best way to do this is to go on an exchange to Germany or another large German speaking country. If your spoken German is good enough, you can enroll in regular university classes, and most large universities will have a course on German sign language.
Learn German sign language online (see Resources). These sites have video demonstrations and classes that you can take to learn how to sign. Some sites also have diagrams of signs that you can access for free just to learn a few different signs in the language.