I only have like slightly less than one year experience with Japanese language, but I have to agree with JimmySeal because those few months slowly taught me the same. I personally use one dictionary, and thats umm Kodansha's Kanji Learners Dictionary.
I agree that its pointless to randomly look up words in a regular dictionary.
My method is like this: I keep reading, If I encounter something unfamiliar, I just look it up in the kanji dic, try to memorize it in a couple of minutes and continue, If it occurs often I insert them into my word/kanji lists and make them into flashcards.
For every kanji I try to write 5 words in which they're used, the most common words I know I will encounter often, or well, more often than the rest.
I also like to choose kanji that looks unique, simply because it will be easier to remember if it looks weird.
As for grammar: I think I have said this before... but umm, screw grammar to hell and back. Really.
It does help some in the beginning, but grammar is only a tool to initiate your own natural learning process, you learn a tiny part of it to be able to understand the basics and build your own foundation, from that point, you must rely on instincts and memory, otherwise you'll become a slave to grammar and won't be able to speak freely for a longer time.
Im talking from my English experience. In truth no teacher was able to teach me anything at all, don't get me wrong, I had two great teachers, but I never actually studied, all I did was speak to them about random crap, and thats it. Other than that I played games, lots of games and mmorpg's.
All my acquaintances from elementary school, most of my mates in high school were/are struggling with grammar, and to tell you the truth, during these years I have seen no progress.
I don't know if its right or wrong... in the beginning I was writing out kanji madly, each like 50 times, but I soon realized that "hey, when will I be required to write kanji?" in a couple of years perhaps, but by time that happens, I'll have it down without a problem. So yeah, Im not learned how to write kanji, only how to read them. In three months time I got myself from nothing (like 20-25 basic kanji characters) to reading manga without frustration, and being able to understand and enjoy it.
There's nothing special about this, I just wanted to point out that If I can do it, most people must be able to do it as well.
Its no magic, because as a secondary effect you just won't be able to write the kanji, tough luck, but knowledge is knowledge and there's no real order in which you must acquire it as long as you plan to learn it all.
Gah, this is long sorry.