If you really want to learn how to climb from scratch the German Alpine club (DAV) might be just right for you. Since June 2013 the club owns its own climbing center in Berlin-Mitte.
At the center you have different areas to practice like a competition wall or an education wall. You can either learn climbing from scratch or deepen your skills.
The center offers different classes like a test class, a starter class that teaches all basics or a pro class for advanced climbing. You can also practice all those classes at Kletterturm on Teufelsberg, which was the first artificial climbing spot by DAV.