Some dictionaries:
http://dict.leo.org/
http://www.dwds.de/
http://www.canoo.net/
Beyond that, I'd recommend you to learn German the same way I learned English and Japanese, i.e. by playing German video games, watching German movies and reading German books.
Most of our movies are shit, but we do make some pretty good vidya. Here's a decent list of notable German games up to 2011:
http://www.pcgameshardware.de/Spiele-Thema-239104/Specials/Made-in-Germany-Die-wichtigsten-PC-Spiele-aus-Deutschland-Artikel-der-Woche-681808/
Text-heavy genres like RPGs and adventures are especially good for learning languages, just don't get discouraged by the fact that you don't understand everything (yet) and simply keep playing.
My personal favorites from recent years are The Book of Unwritten Tales and The Whispered World, both of them point&click adventures:
https://www.youtube.com/watch?v=BKyeyhR6OHs
https://www.youtube.com/watch?v=aB_EHtXHjO8
The Gothic series (RPG) and Deponia (adventure) are some other games that are pretty popular, although I haven't played them myself.