When writing or reading in Japanese, there are three writing systems that need to be understood (four if you include rōmaji, the Roman alphabet). All these writing systems are in widespread use, and anyone seeking to read Japanese needs to know how to understand them.

Kanji is the hardest to learn due to the sheer number of symbols it includes. Adopted from the writing system used in Chinese, kanji represent words as symbols or groups of symbols, sometimes referred to as 'ideograms'. Kanji are also used to write Japanese names. There are over 6,000 individual kanji, although only around 2-3,000 of them are in common usage, and it is possible to get by on a set of 1,945 'everyday' kanji (the jōyō kanji). An interesting characteristic of kanji is that they can usually be pronounced in several different ways.

Hiragana is one of the two Japanese 'kana' (along with katakana); syllabic writing systems (i.e. based on syllables rather than whole words) used in Japanese. As there are just 46 basic characters to learn (along with rules for accenting and character combination), it is fairly easy to get to grips with.

Katakana is very similar system to hiragana. Also a phonetic system with 46 basic symbols, the same rules of writing are used, but the characters themselves are different in appearance, typically quite angular compared to the rounded strokes of hiragana. Katakana are used mainly for writing 'loan words' that have been borrowed from other languages. This includes the names of foreign countries, cities, etc., new or borrowed words (such as 'computer', 'ice-cream', etc.) and non-Japanese names. Loan words, when written in katakana, have to be spelled phonetically using the Japanese rules of pronunciation and the set of syllables available. For example, "hamburger" is written "hanbaagaa".

The use of honorific language in Japanese is often a source of confusion, and can make learning spoken Japanese quite difficult. Basically, honorific language is the use of different words (usually different verb endings) to express respect towards the person you are addressing. Depending on who you are addressing, you may use a colloquial, a more formal or a very formal mode of speech.

One element of honorific language that many non-Japanese-fluent anime fans are familiar with is the use of name extensions. It is common to add a short extension to a person's name when addressing them, the extension used depending on that person's relationship to you. In the Japanese-language version of Tenchi Muyo!, for example, Tenchi often refers to Ayeka and Ryoko as "Ayeka-san" and "Ryoko-san", while he refers to Sasami as "Sasami-chan". A short list of common name extensions is included below;

-san: A standard polite extension. May also be used when not particularly familiar with a person.
-dono: A respectful extension. Archaic, but still found in anime (e.g. Washu's "Tenchi-dono").
-sama: A very polite extension. Usually used to address very important people or people you are very close to.
-chan: Usually only applied to very young people, particularly young girls (or cute animal mascots!), or someone to whom you are very close. Washu insists on being called "Washu-chan" (translated as "Little Washu" in the English dub), even though she is actually much older than everyone else in the series!
-kun: Usually applied to males younger than yourself, particularly young boys. Also used by teachers addressing male students, and between close male friends. Sasami switches from calling Ryo-Ohki "Ryo-chan" to "Ryo-kun" when she finds out his true identity in the penultimate episode of Magical Project S, reflecting her change in attitude towards him.
-sensei: Used when addressing your teacher or master (school teacher, martial arts master, etc.).
-sempai/senpai: Can be used as an extension (e.g. "Tenchi-sempai") or on its own, and is often heard being used between students in anime to address seniors (though its use is not restricted to the classroom — it is often used in the workplace as well). Note: Although there are two different spellings shown here, they are not different words, merely different romanizations of the same word.
-kōhai: The same use as senpai, but used to address juniors.
-niichan/-neechan: This one is included as a special note since Sasami uses these extensions as terms of affection to address Tenchi and the girls. They roughly translate as "brother" and "sister". Examples are "Tenchi-niichan" (big brother Tenchi) and "Ryoko-neechan" (big sister Ryoko). These terms can also be used on their own —"oniichan" and "oneechan" — which Sasami also uses. Neiju also adopts the term to refer to Seina in Tenchi Muyo! GXP, calling him "Seina-oniichan", again to express her attitude towards him.

Irasshai
Irasshaimase
Yōkoso

Konnichi-wa
Konban-wa
Ohayō gozaimasu 

おたく

Although the original meaning of the word "otaku" is "your home" or "yourself", in popular Japanese slang it is used to describe someone who is a devoted fan of something (of anything, not just anime or manga). Its use in Japanese is actually somewhat insulting (roughly equivalent to calling someone a "fanboy/fangirl geek"), but outside of Japan some anime and manga fans have taken to using the term to describe themselves (i.e. "I am an otaku", to mean "I am an anime fan").

Bowing as a greeting is perhaps the most well-known behaviour specific to oriental cultures. In Japan, bowing (ojigi) is used to greet, especially on a first meeting, when making a request, to express gratitude, to say goodbye and to apologize for something. The correct way to bow is to keep your arms by your sides and bend at the waist, keeping your back straight. A bow of 10°-20° from vertical is normal for most situations, but when expressing greater humilty, such as when apologizing, a deeper and longer bow is more appropriate. Of course, the simple bow is often taken to the extreme in anime and manga, usually for comical effect. Characters are regularly seen bowing in the Tenchi series — in the example screenshot from OVA episode 13 (left), Ayeka bows to Funaho (notice that Ayeka bows deeper than Funaho to express her respect).

As well as ojigi, there is zarei, a more formal bow that a person may use to welcome someone to their home. This is performed in the kneeling position, with the host placing his or her hands flat on the ground in front of them. Again, the depth of the bow expresses the degree of humility. In episode 11 of Tenchi in Tokyo, we see Sasami performing the deepest zarei, where her head touches her hands, when she has to tell Katsuhito about one of his statues getting broken.

A gesture often seen in anime and manga is yubi-kiri, the linking of the little fingers of the right hand. This is often done by children when making a promise to each other. We see Sasami and Ryo-Ohki link fingers in this manner in episode 26 of Magical Project S after Ryo-Ohki promises to come and visit her.

A character sneezing when someone is talking about them behind their back is a fairly common sight in anime and manga. This is based on a Japanese superstition that states if you sneeze for no apparent reason, it means that you are being talked about (or particularly, talked about in an insulting manner). This is comparable to the superstition about one's ears burning that may be more familiar to Western viewers. In episode 2 of the Tenchi Muyo! OVA series, Ayeka is seen to sneeze while aboard her spaceship when, at the same time on Earth, Ryoko is warning Tenchi about her ("She's so dangerous and mean..."). We see Seina and Ryoko Balouta sneeze for the same reasons in episodes 25 and 26 of Tenchi Muyo! GXP.

Nosebleeds amongst male characters are a common phenomenon in comedy anime, invariably occurring when the character is confronted by a naked female or similar arousing event. There are several explanations for this visual method of representing the character's excitement or embarrassment. The most obvious is that this is a result of the increase in blood pressure. Indeed, the idea that libidinous thoughts and sights cause nosebleeds is an old wives' tale in Japan which has become absorbed into the visual language of anime and manga. Additionally, there is a theory that the "explosive" nosebleed (a variation that appears in many comedy anime and manga, and which is used frequently in Tenchi Muyo! GXP) implies ejaculation.

In episode 4 of the Tenchi Muyo! OVA series, Tenchi's lecherous father Nobuyuki attempts to peep into the women's bath at the hot springs resort. Before doing so, he ties a towel around his head as "the traditional attire for peeping". Ryoko does the same thing in episode 7 when she attempts to sneak into Tenchi's bedroom, and Seina and his roommates wear towels on their heads when they are sneaking out of their dorm after curfew in episode 5 of GXP. Again, this is a staple of comedy anime (regular readers / viewers of the classic Ranma� manga / anime series will be familiar with Happosai wearing a towel or handkerchief in the same manner when he is out stealing underwear). Far from being "peeping attire", the towel is part of Japanese rural clothing tradition, and would have, in this context, been used as a form of disguise. For example, if a male servant of a large household wished to make a pass at a female servant (or indeed the master's daughter), he would use a towel in this manner to obscure his face. This meant that, in the event of their employer finding out and disapproving, the young lady would simply be able to deny seeing his face clearly, thus avoiding embarrassment, dismissal or punishment of the offending parties.

In episode 11 of the Tenchi Muyo! OVA series (The Advent of the Goddess), Zero, Ryoko's double, performs a gesture to stop herself being embarrassed. She draws a symbol on her hand with her finger then mimes eating it. This is a symbolic Japanese gesture to calm oneself down that occasionally crops up in anime. The performer draws the kanji 人 ("hito" — person / human) then mimes eating it as if to "swallow" their nervousness. Although we cannot see clearly what Zero draws, she does mutter "hito", confirming this.