You already know anime and manga from above. Here are some other, re-occurring words and phrases you'll come across while watching anime or talking about it with friends.
Some of these words or phrases have been mentioned before in The Anime Dictionary.

1.	Baka!	"You're stupid!"
2.	Chara	character
3.	Chibi	Short, tiny. A chibi character may naturally resemble a super-deformed character, where the entire body has a smaller, squashed, cuter appearance.
4.	Dojinshi	Generally fan stories pertaining to a specific series. Could also be any series specific fan art.
5.	Hentai	Abnormality. Sexual perversion. Used also to describe a certain class of anime, manga or otaku (as in "H-Anime").
6.	Idol	(a) Certain people and characters transcend being something that you're a fan of. When you start worshipping them, adorning yourself in their image, collecting dolls, images or cards of the character, they've become your idol. (b) Singers with a major role in a series (Minmei from Macross for example).
7.	Japanimation	American slang for for Japanese animation. Similar to other less than ideal contractions like "blaxsploitation" and "teensploitation." It's best to either to use the full "Japanese animation" or shorter "anime." Don't talk about "Japanimation" to an otaku.
8.	Kawaii	cute
9.	Henshin	Transformation. Used to describe the sub-genre of special-effects shows featuring super-hero transformations (Kamen Rider or Metal Heroes). Also used to describe transforming mecha (Henshin Robo).
10.	Mecha	Just about anything mechanical: weapons, vehicles, robots, but usually not items like pencil sharpeners or ceiling fans.
11.	Nani?	"What?"
12.	Nihon	Japan.
13.	Otaku	Anime fanboy or fangirl. Generally a good thing in America, apparently closer to being a geek in Japan. If you're wondering if you've become an otaku take a look at Are you an Otaku?
14.	OAV/OVA	Original Video Animation: an anime direct to video release, anime made only for the video market. Direct to video releases are common in Japan, while still a rarity in America. Unlike the US, where Direct to video movies are still often seen as a reprieve from what would've been a disastrous theatrical release, OVA's in Japan can be big events unto themselves.
15.	Seiyuu	Anime voice actor or actress.
16.	Sentai	Task-force. Used to describe the task-force genre of live action TV series, including Zyuranger/MMPowerRangers and DaiRanger. Some American fans have been known to use this as a synonym for special-effects shows when they really mean to use tokusatsu.
17.	Tokusatsu	Special-effects. As one might use it in English, tokusatsu is used to describe a super-category of live action super-hero shows (Kamen Rider/Masked Rider or Zyuranger/MMPowerRangers) and giant monster movies (Godzilla or Mothra).