Hmm, let's see...
I started off with learning katakana by playing a GBA game, namely Tales of World: Narikiri Dungeon 3. No English version of the game was available, so I had to play in Japanese. Almost all skill names were written in katakana, and were altered English (e.g. fireball written as ファイアボール; faiabooru). I then forced myself to memorise all the katakana letters from its table. As for hiragana, it wasn't much different - I forced myself to memorise all the letters; took me like 2-3 hours. Make it 2 days with all the exercises.
Then I watched animu and listened to Japanese songs - that's pretty much how I started recognising words and eventually sentence structures etc. Dictionary was never really reliable, so I did lots of analysis on my own to decipher structures, patterns, and other essences of the language. As I learned how to compose sentences, I started trying to communicate in Japanese with various people. Of course, my sentences were broken when I started, but as long as I had someone fix them and explain my mistakes to me, it was always fine.
It still continues up until now - well, currently I'm majoring Japanese literature, so how I learn is out of question, but I still do much self-learning. Not to boast, but I've observed that most of my friends of the same major lack the skills and sense needed in dynamically phrasing out sentences. Such things aren't something you can learn academically, but kinda depend on your feel. That's how studying languages is, after all.
Animu is actually a very good way to learn structures as well as informal expressions and words. When you're good enough to watch raw animu, try moving on to visual novels. Start off with simple ones with short and simple dialogues, preferably something with a simple theme like school romance. That's where you will most likely encounter sentences that get used often on daily occasions.
Hope this helps somewhat. Good luck.
