Japanese is written with hiragana, katakana, and kanji. Numbers can be written in either Arabic numerals or kanji. A few words, such as OL ("office lady"), are usually written in the roman alphabet. Note that all Japanese characters have fixed stroke orders for when they are written by hand, so if you want to learn them it is best to use a proper textbook.

There are many websites which have hiragana and katakana tables and lists of kanji, as well as tools to help you learn them. Charles Kelly's website is a good place to start.

Hiragana

Hiragana have a simple, curved appearance. Some words are written entirely in hiragana. Verbs and adjectives usually consist of a kanji, which carries the meaning, followed by hiragana, which constitute the inflection.

Katakana

Katakana are simple angular characters with straighter strokes, mainly used to write words of foreign (but not usually Chinese) origin. It is useful to be able to write your name in katakana. To take a simple example, "Chris Hale" would be written クリス ヘイル and pronounced as Kurisu Heiru.

Kanji

Kanji are the characters that have either come directly or been derived from Chinese characters. They tend to have many more strokes than hiragana or katakana, all of which are supposed to be written in a particular order.  Literate adults are expected to know at least 2000 characters.