Japanese is written using a combination of "Kanji" and "Kana" characters. "Kanji" are Chinese symbols, used to represent words or ideas - either on their own, or in groups. "Kana" are more like the alphabet used by English speakers, in that they represent sounds, not concepts.
Just as the alphabet is made up of upper and lower case, Kana is split into Hiragana and Katakana. Katakana is mainly used for words of foreign origin, such as "America", "banana", or "pink":
Hiragana is used for anything else - words, grammatical particles, etc. It can be even be used as an alternative to Kanji, for situations where a word is known, but the Kanji symbol to represent it isn't. For example, consider the word "nihongo", which means "Japanese language" in Japanese:
TODO: Explain alternative transliteration systems (Hepburn system + Kunrei-shiki) here...
TODO: Explain っ/ッ and ー here.
The basic "fu" (ふ or フ) sound can be modified by a small vowel character:
Examples: Family Mart
ラリルレロ are used for both ra/ri/ru/re/ro and la/li/lu/le/lo.
Usually replaced with B.
Alternatively, can be written as a "voiced" U, with a small vowel following it, similar to fa/fi/fu/fo
Katakana characters for va/vi/ve/vo were defined, but never actually used. They are represented as "voiced" versions of the wa/wi/we/wo katakana characters.
The "wa" kana (わ/ワ) are pretty much the only real "w" characters in Japanese. The "wo" kana (を/ヲ) are actually pronounced more like "o", and are rather less common than the usual お/オ kana.
The "wi" (ゐ/ヰ) and "we" (ゑ/ヱ) kana are obsolete and are almost never used. If they are used, it's generally for "effect" rather than pronunciation; they sound identical to "i" (い/イ) and "e" (え/エ) in modern Japanese. For example, ヱヴァンゲリヲン would be transliterated as "Evangelion", not "Wevangelion" (also, notice that ヲ is used instead of オ for the "o" sound - as with ゑ, the "w" isn't actually pronounced).
Instead, w- sounds (other than "wa") tend to be represented as a "u" followed by a small vowel:
For example, "wetsuit" would be written as ウェットスーツ
Usually replaced with S or Z.
Gareth = Garesu
The = Za
A "ye" sound can be written as a katakana "i" followed by small "e" character. For example, "yellow" would be written as イェロー
Except for "n" (ん/ン), all syllables end with a vowel sound (ん/ン is also unusual in that it cannot be the first syllable of a word - probably for this reason).
As such, it's common for words to have vowels added on to the end when they're imported from other languages. For example, "test" becomes テスト ("tesuto").
couple of exceptions to the usual rule:
How can you tell when they're being used as particles? Context.