Japanese is spoken and written using a system of 46 syllables. In fact, many aspects of the language revolve around the way the syllables work. Japanese has five vowels: a, i, u, e, and o when romanized. A is pronounced as in "ah", i as in "eat", u as in "food", e as in "eh", and o as in "oh". The vowels are short and clipped when compared to English. This is because there is a distinction between long and short vowel sounds; short vowel sounds count as one syllable, and long sounds count as two. The pronunciation is the same, it's just that the sound is held for longer.
The Japanese vowels combine with consonants to form syllables. The main consonants are k, s, t, n, h, m, r, y, and w. The syllables are grouped together by which consonant they use. For instance, the syllables ka, ki, ku, ke, and ko form a five-syllable group.
The Japanese "r" deserves special attention: it is not the back-in-the-throat r of the French language, nor is it the purring, back-in-the-throat r of English. It's more like an odd cross between an l and a d; it's pronounced kind of by flipping the tongue against the back of the teeth. Some people romanize this sound as an "l", and indeed some Japanese pronounce this sound like an English "l".
The syllables and their groups are:
You must have noticed a few exceptions to the "syllable = consonant + vowel" rule. First is the s row. The second syllable is pronounced "shi", just the same as the English pronoun "she". The Hepburn system of romanization (that is, writing Japanese in Roman or English letters) writes this as "shi", while the Japanese National system writes it as "si". Among native English speakers this is usually written as "shi"; most English speakers seem to prefer the Hepburn system, but the Japanese National system better represents the relationships between syllables.
The t row of syllables has two exceptions. The first is the second syllable, pronounced "chi", just like the English word "cheese" without the se. This is written "chi" in the Hepburn system and "ti" in the Japanese National system. The third syllable can be difficult for native speakers of English and comes best through practice. It is written "tsu" in the Hepburn system; it is pronounced by putting your tongue on the back of your teeth, like you're about to say a t sound, and then saying "su". The Japanese National system writes it, of course, as "tu".
The third syllable in the h row is written "fu" in the Hepburn system. The "f" is not pronounced like an English "f", where the top row of teeth is touching the lower lip (they do, or almost do, if you pay really close attention to how you speak ^_^; ); it's more breathy. You should blow lightly through your open lips. The Japanese National system writes this as "hu", which isn't that far off; it really is kind of like a really breathy h.
There is no "yi" or "ye" syllable in Japanese, at least not anymore. Also, the "wo" syllable is pronounced "o"; it is used as a grammatical marker.
The syllabic n is just that: an "n" sound that takes up its own syllable. It's pronounced just like an "n" without a vowel.
In the Japanese writing system, there is a mark that goes over kana that changes the pronunciation slightly. This mark is called a "dakuten", and it looks somewhat like a diagonal double quotes mark ("). Think of it as making the consonants softer. It changes "k" sounds to "g" sounds, "s" sounds to "z" sounds (exception: "shi" changes to "ji"), "t" sounds to "d" sounds (exception: "chi" would change to "ji", but you really don't see that; "tsu" usually changes to "dzu" but is usually romanized "zu"), "h" sounds change to "b" sounds. Also, there is a "handakuten" mark that looks like a little circle that is only used on h syllables; it changes them to p sounds.
Certain syllables can be combined to make more "complex" syllables. Specifically, "mi", "ni", "shi", "ji", "chi", "ri", and "ki" can be combined with "ya", "yu", or "yo". This comes out like this: