Besides the three forms of writing (kanji, hiragana, katakana), Japanese is sometimes written in Romaji. Romaji is primarily used for the convenience of foreigners. With Romaji, one can read Japanese without knowing any Japanese writing system. Although there are several systems of Romaji, the most widely used is a modified Hepburn system.
All three types of Japanese characters are designed to be written in vertical lines, from right to left, but they can be written horizontally as well. Years ago, almost all Japanese writing was vertical, but the horizontal style has slowly become more popular since it is easier to include Arabic numerals and passages from other foreign languages. However most newspapers still retain the vertical style.
Check out some questions about my "Question of the Week".
- Vol. 4: Can I survive in Japan without knowing Japanese writing?
- Vol. 12: Which do you commonly use to write Japanese: vertical or horizontal writing?
- Vol. 27: How many kanji do I need to learn to read Japanese?