What I will try to show you here is the "kana", that is, the Japanese alphabets. This should at least allow you to have some fun figuring out exactly what it says on the front of your anime videos and confuse your friends by writing little notes in hiragana and leaving them about.
Yes, you heard correctly: alphabets. Japanese has three alphabets: Hiragana, Katakana, and Kanji. Hiragana and katakana are phonetic, and can be directly transliterated into english (more or less). They are what are actually called "kana". Kanji, on the other hand are borrowed from Chinese. They express a single idea or concept with each character and at the same time have a component of pronounciation.
Hiragana and katakana are fairly simple. Kanji is not. After you've finished reading this page and have arduously practiced reading and writing for a few weeks you will be able to use hiragana and katakana with reasonable ease. To do the same with kanji would take months, probably years. You would have to memorize about 1800 different characters to be basically literate. Therefore, I'm not even going to try to show you the kanji (beyond telling you the characters at the top of this page are the kanji for "kana").
Romaji is a word for writing Japanese in English characters. There are several systems for doing this. The one I am using here is the Hepburn system with the slight modification that long vowels are written using a literal transliteration, eg. in "sou desu ne" ("That's true isn't it?") the "ou" is actually a long 'o'. If you don't know the different systems I advise you not to worry too much. If you do know the difference then you probably don't need this guide anyway.
Gojuuonzu is Japanese for "table of fifty sounds" (literally "five tens sound illustration", but you get the idea). It is a way of organizing the phonetic alphabets. Here is the gojuu on zu in romaji:
a ka sa ta na ha ma ya ra wa n i ki shi chi ni hi mi ri u ku su tsu nu fu mu yu ru e ke se te ne he me re o ko so to no ho mo yo ro o
Remember that pattern, because that's how I will show you the hiragana and katakana characters. The rows are called "dan", thus a-dan, i-dan, u-dan, e-dan and o-dan. The columns are called "gyo", thus a-gyo, ka-gyo, sa-gyo and so on.
In a Japanese dictionary the alphabetical order is top to bottom in each dan, from left to right across the gojuu on zu (as I have shown it anyway). Thus first come words that begin with 'a' then 'i' and so on until 'o', then comes 'ka', 'ki', 'ku', etc... Note that you may see this table written in a different order elsewhere, such as in some textbooks. For example, with the a-dan on the right is much more natural for native Japanese speakers. The important thing is not the way the table is laid out, but remembering the order (a, i, u, e, o, ka, ki, ku...).
Ok, ok, so there aren't fifty sounds in the table of fifty sounds, and 'o' is in there twice. Well, first of all 'n' doesn't count, because it is considered more or less silent. The missing sounds like 'yi' and 'we' simply are not used in Japanese anymore. They used to be there, but now they're not. And the two 'o' symbols... The one in the 'wo' place is a particle and only gets used as a separate word (and in certain circumstances is pronounced 'wo.')
Pronunciation of Japanese is fairly simple once you get the hang of it. Once you translate Japanese characters into romaji the pronunciation is completely phonetic (almost).
Each symbol in the gojuuonzu is a syllable, and each syllable in a word is given equal time (roughly). Thus "okii" ("big") is three syllables o-ki-i.
One major difference is 'r'. The sound written in romaji as 'r' is actually about halfway between 'r' and 'l'. This is why, if you translate the way "Laputa" is written in Japanese it comes out as Raputa (actually Rapyuta, but that's another topic).
For vowels
'I' and 'u' are often "de-voiced", that is, whispered or dropped altogether. Thus "nani desu ka" ("what is that/it?") often sounds like "nan des ka". There are lots of other rules for subtle variations in sounds, but this should be enough to help you get started.
These pronunciation rules are based on those given in the book Conversational Japanese by Ichiro Shirato, revised by Hiroko Storm, Ph.D.
Shown here is the gojuuonzu for the hiragana. This is the more common phonetic alphabet. It's most often used for writing short words like particles or different endings on words. If you're lucky some of the kanji you see will have hiragana written over or next to them in smaller letters (called "furigana"). This tells you (or the young child it was meant for) how to pronounce an otherwise unfamiliar kanji.
This is the gojuu on zu for the katakana. Katakana is actually seen more often in anime circles than hiragana. That's because katakana is used for foreign or borrowed words. Words like "supercomputer" and "missile" are borrowed with almost no change in pronunciation in Japanese, and they are written in katakana. Often the names of imaginary/foreign things in anime like "Laputa" or "Macross" will be written in katakana as well.
Symbols of the ka-gyo, sa-gyo, ta-gyo and ha-gyo can be changed to voiced equvalients by writing two short strokes on the upper right of the symbol. Ka-gyo changes to ga-gyo, sa-gyo to za-gyo, ta-gyo to da-gyo, and ha-gyo to ba-gyo. For example, below is the ka-gyo, and under that the ga-gyo.
Watch out for shi, su, chi and tsu. Both shi and chi change to ji, and su and tsu both change to zu. The symbols are different but their romaji equivalents and their pronunciation is the same.
The ha-gyo can also be changed to the semi-voiced pa-gyo (shown below) by adding a small circle to the upper right instead of two strokes.
Although I've only shown the hiragana here the same thing can be done with katakana. In fact there are some unofficial variants which allow such things as writing a "v" sound (not normally possible in Japanese) with a katakana "u" and the voiced syllable mark.
A long vowel in Japanese is not the same as a long vowel in English. The sound of the vowel does not change, all that happens is the sound is held for an extra syllable. Thus "bataa" (butter) is "ba-ta-a" (yes, they borrowed it from English).
Most long vowels can be written in hiragana by adding the same vowel symbol immediately after the symbol which ended in that vowel. The exceptions are 'o' which is followed by 'u' to make it long and 'e' which can be followed by 'i'.
In katakana long vowels are written by following the syllable with a dash (or a vertical bar if you are writing from top-to-bottom instead of the "westernized" left-to-right style).
There are almost no occurrences of long 'e' in Japanese.
The double consonants you may see in romanized Japanese like "kakkoii" ("cool!") indicate that there is a small pause between the syllable before the double and the one after ("ka koii"). Usually if you pronounce it like you would naturally it will come out right. To write these pauses in hiragana or katakana write a small 'tsu' where the pause will go.
e.g. 
Certain symbols from the i-dan may be followed by a small symbol from ya-gyo to form a "contracted syllable." Both symbols together represent one sound. Thus ki + small ya = kya, shi + small yu = shu, and so on. Below is a list of all the contracted syllables.
Particles are small parts of speech in Japanese. In order to confuse gaijin the Japanese write some particles with symbols which represent different sounds.
Japanese can be written two ways: left-to-right and top-to-bottom in lines or top-to-bottom first and then right-to-left in columns. Punctuation and such symbols as the long vowel marker in katakana will change slightly depending on how a passage is written.
To add to the confusion Japanese is generally written without spaces between words. This is one reason why Kanji actually make it easier to read Japanese.
The information in this page was obtained mostly from Easy Hiragana by Fujihiko Kaneda. The images of katakana, hiragana, and kanji were generated using JWP version 1.1, a free Japanese Word Processor for Windows, by Stephen Chung, available here.
The original version of this document was written by Colin Peters.