Japanese writing and printing uses three character systems: kanji (Chinese characters or ideograms, and two kana (syllabary systems): hiragana and katakana. Japanese texts can be written either in " Western" style, i.e. in horizontal rows from the top to the bottom of the page, or in traditional Japanese style, i.e. in vertical columns from the right to the left of the page.

Kanji

Although the Japanese language itself is not related to Chinese, kanji - Chinese characters - were adopted in the sixth century (before which time Japan had no writing system). As each kanji is a unit of meaning, there are thousands of them. Because of the way they have been adopted into Japanese, a single kanji may be used to write one or more different words. This means that kanji can have several different "readings". The correct reading depends on context, intended meaning, use in compounds, and even position in the sentence. Some common kanji have ten or more possible readings.
2000 - 3000 kanji characters are used in newspapers and magazines. The set of "official kanji for everyday use" is 1,945 characters.
The most cultivated and classical literature uses a wide variety of kanji, many of which are relatively unknown, particularly among younger Japanese.

In this video, artist Hirokazu Kosaka shows a few of the basics of Japanese calligraphy (Indianapolis Museum of Art)

Hiragana

These characters are a syllabary, in the sense that each character stands for a syllable, not a word or unit of meaning: usually a consonant and a vowel combination. Hiragana is used for all normal Japanese words for which there is no kanji; or the writer doesn't know what the kanji is, or thinks the reader won't; or where using the kanji character would be too formal or literary for the context.

Katakana

This syllabary is usually used for transcriptions of foreign words, technical and scientific terms, Japanese company names, emphasis (like italics), or to indicate words spoken in a foreign or strange accent (eg. in manga comics)

Even with all these characters to indicate sounds, the Japanese language (and the speaking habits of Japanese people) have problems with certain sounds from foreign languages.
The only consonant which can exist on its own in Japanese, for example, is ""n". The words "cheese", therefore, becomes "cheezu".
The "l" sound is notoriously difficult; ra/ri/ru/re/ro exists, but not la/li/lu/le/lo. So the name "William Trollope" would come out sounding more or less like "wi-ri-a-mu tu-ro-ro-pu", depending on how adept the speaker is at pronouncing non-Japanese words.