Couple thousand kanji, plus a double alphabet of syllables
A couple thousand JUST for the most basic kanji, the amount you're expected to know after completing elementary education. For each kanji there are usually 2 ways of reading it, derived from Japanese and Chinese, called "On-yomi" and "Kun-yomi". Different readings can be combined in different ways to form different meanings.
Unabridged, there are over 7000 Kanji that can be used, though you'll need about 3 thousand or so to be able to read a Japanese newspaper without reference.
And then there's the kana alphabets, which have a few dozen symbols to represent phonetic sounds and particles.
If you want to learn to do fan translations of manga and the like expect to be encountering a lot of strange, esoteric kanji, and many foreign loanwords. As mentioned, the New Nelson is invaluable because of its comprehensiveness.