How do you use the subjunctive mood?

In the German language there are two types of subjunctive: the Konjuntiv I and Konjunctiv II. The first form is used in reported speech, in order to report something that may or may not be true. The Konjunctiv II is used more often in everyday life, in order to show that something is contrary to reality, to request something in a polite way, and to express wishful thinking.