Now that you've got the phonetic symbols down, it's time to tackle the hardest part: kanji. There are said to be about 50,000 kanji characters in Japanese, but don't panic, you only need a small fraction of those to be literate. The Japanese Ministry of Education has a list of about 2,000 characters called the jouyou kanji which are taught in elementary and secondary school. If you can master that list, you will be able to read and write well enough for daily life.
If 2,000 still seems like a daunting number, remember that many of them are very simple pictographs. For example, 山 (yama) or mountain, looks like its meaning. Many other evocative characters like 木 (ki/tree), 口 (kuchi/mouth) and 門 (mon/gate) are common radicals in other more complex kanji, so you can sometimes guess the meaning of a new character by the sum of its parts. For example, the verb 聞く (kiku/listen) combines the symbol for ear with the symbol for gate.
An excellent resource for learning the kanji which uses this pictoral approach is James Heisig's Remembering the Kanji. For an online Japanese-English dictionary that includes a fuction for searching for kanji by radicals, try the useful Denshi Jisho. And for more help on studying kanji and some free kanji flashcards, see this article.