In my opinion, the best way is to let somebody lock you up with 15 other Germans desperate to learn Dutch (for admission to university) and a teacher for a month and then stay in the Netherlands when you get out again. That's what I did, and I think it worked pretty well (if I may say so myself).
If that's not an option, I think you could just go about it like you would go about starting any other language, and skip the boring parts (looks like German, German, German ... continue on page 50) - that's what they did in my Dutch course, at least. Also, just practising the things you want to would probably help a lot. Try to translate short text or transcribe audio (I'm sure people on here will be happy to help you correct it). Or read a book you already know in German, preferrably with an audiobook alongside it. And as Muisje said, having a good grasp of orthography and a feel for the most common sound changes helps a lot. (At first glance, "zwijgen" doesn't look familiar, but if you know that it would be spelled something like "sweichen" in German and that word-initial S
in Dutch is usually s and g corresponds to x, "schweigen" is the obvious translation.)
Sorry, it's all not terribly innovative, but I don't think there's any perfect method.
(There seem to be some books on learning to read Dutch quickly aimed at Germans specifically though. Don't know any titles, unfortunately.)