I originally tried to learn the kana the way I'm sure a lot of you did, in dictionary order, a i u e o, ka ki ku ke ko, et cetera. Then I thought about it a bit, got a hold of a couple PDFs containing Heisig's remembering the kana, and learned them out of order. I didn't use the mnemonics the books are famous for, just learned them in that order. I spent a day on Hiragana, and a day on Katakana, with only a few hours of actual study time. Ever since then, I've been able to read both scripts without any trouble. That's right, just changing the method, instead of taking more than a month to learn them, they each took only a few hours. They're really easy if you study them this way, at least in my experience.
Right after learning them, I would quiz myself at random times. I'd wake up and immediately write the scripts down in their entirety. I'd transliterate songs from romaji to kana and back with a pencil and paper. I'd read text, even if I couldn't understand what it meant just yet. This greatly improved my recognition speed, and at this time I can read kana at least as fast as I can speak it if not faster.
As for the language, I taught myself a fair amount of grammar through various means and through Tae Kim's guide. I learned a lot of different words just by listening. I can speak, read, and write at least enough to get around (I put that to the test this past summer, staying a month in Japan alone).
Going a bit off track here; the point is, those of you learning the kana, don't learn them in dictionary order! This is the most common mistake I see. People who learn them this way tend to have trouble remembering them individually, which makes them harder to memorize and slower to recall as a whole -- they remember them in sets. When you're trying to read/write "ke", you should NOT remember "ka", "ki", and "ku" first. Do you remember a, b, and c before you remember d in English?
Also, it's not that important I suppose, but I don't recommend learning the voiced/plosive versions until after you have all the core characters down. That is, dont bother with "ga", "da", and "pa" until after you've already learned everything, including their sources, "ka", "ta", and "ha". They'll come easily enough later.
Anyhow, I never really intended to post here, but seeing so many people looking to learn kana and taking the usual route, I thought I'd offer another one I found so much easier and more effective.
Have fun.