Learning grammar?

I've been learning german for the past few months and I've picked up some basic, just a selection of nouns, verbs and adverbs - plus a few standard phrases. I want to start using all these words I've learned to form real sentences!

I picked up a German grammar book but I've found it to be terribly confusing. It's not the book's fault but just that there are so many rules that I get overwhelmed, especially with teh Dativ, Genitiv, Akkusativ and Nominativ cases.

I was wondering if there is a simpler way of learning grammar? I understand the best way to learn words is to learn as if you were a child - presented with an object and say what the object is. Thats what I'm doing at the moment (similar to Rosetta Stone). Is there some similar system I can use for grammar? When I was a child learning to speak I don't remember trying to learn a list of rules on how to form sentences - I just picked it up from speaking and listening. Is that even possible now learning a different language as an adult?