There are 3 character sets in simultaneous use at all times. Hiragana and katakana are syllabaries that each have 46 characters and cover all the sounds available to the language.
Kanji are a [redacted]. Your are illiterate until you can read 1000 or so. Kanji are composed of any number of 216 radicals which are the basic building block kanji. The best part is that each kanji has 2 or more pronunciations: the Chinese pronunciation and one or more Japanese pronunciations.
Schoolchildren are considered adequately literate when they know 2000 kanji.
Oh. There is also romaji, which is the official approximation of Japanese using the English alphabet. No clue how they typewritered, but this is how the majority type on computer. They have to type in the romaji and the computer autocorrects it to Japanese characters.