There are two excellent sites to help speakers of German learn English, Englisch Hilfen and Englisch Lehrbuch.
Englisch Hilfen provides users with detailed vocabulary lists and grammar explanations organized by theme, as well as links to locations where Germans can study English abroad, sections on business English, and language exercises, tests and games.
Englisch Lehrbuch offers its users more than 30 detailed chapters on the English language, almost all of which have audio files for download. The audio resources can help improve listening comprehension and pronunciation skills. The site also provides interactive virtual tours of English-speaking cities, exercises, and the ability to chat with other users.
Many textbooks are package with helpful audio resources. Those include "Englisch ganz leicht" by Brian Hill and Marion Geddes as well as "English ganz leicht: der neue Sprachkurs" by Steven Fox. Both of those resources introduce students quickly to conversational, useful English based on real-life situations.
The English-speaking world is a major producer of entertainment, including films, television and music. By incorporating those multimedia resources learning the language, a German speaker can improve his or her listening comprehension and pronunciation, and also learn idiomatic English. That style of learning might also keep learners engaged when book learning might become uninteresting. Singing along to English-language CDs and watching American films with German subtitles also can be helpful.
Although English and German share many words in common, there are also several words that lead speakers of both languages astray. "Handy" in English is an adjective for something nearby or useful, or for someone who is skilled at manual labor, and has nothing at all to do with cellular phones, which is what "Handy" means in German. Even some commonly spelled words can be misleading: "also" means "in addition" in English but "thus" in German. To learn more about what words are and aren't the same between English and German, see Resources below.
It's a good idea for German-speakers to keep organized notes of the vocabulary and grammar items they learn so that they can make reference to them later. By using a variety of resources to gain wide exposure to the English language, and aiming for about an hour's study every day, the topics will be kept fresh in their minds and will help them make quick progress.