Nobody's mentioned it, but you will pick up a lot of Japanese phrases from watching subbed anime. Anyone who's seen more than 50 anime knows what doushite or betsuni or sasuga or yokata means because they're phrases used all the time and often in isolation.
Obviously you'll be watching with subtitles, but some parts of the language won't necessarily be translated, so you should be aware of them. The only parts of Japanese I'd say are worth knowing before watching anime are honorifics and how names work, but these are so basic that if you're using a site like wizchan you must already have some vague idea. I'll start with names.
First of all, the name order is the opposite of English: family name, then given name. The man who Westerners call Hideaki Anno would be Anno Hideaki to a Japanese person. Yukio Mishima is Mishima Yukio.
You call somebody by their family name to be polite, but keep in mind the Japanese are extremely autistic about politeness. I would address my classmate (but not friend) by their family name plus an honorific, but I'd address my best friend by their given name. Romance anime, particularly with shy/awkward protags, will make a big deal out of them asking each other if they can address each other by their given names, and they'll blush like mad as he addresses her as Akane-chan rather than Mizuno-san.
Before I move on to honorifics I should mention that sometimes succubi will have -n put at the end of their name for cutesy reasons, like Megumi becoming Megumi or Minori becoming Minorin.
Second of all, you probably noticed the -chan and -san suffixes. These are honorifics, which denote the relationship between the person speaking and the person being referred to and can be used to show respect - think if Mr, Mrs, adding '-y' to the end of something to make it cutesy, etc had a bigger role. While they aren't the only ones, I'd say there are three essential ones that you'll pick up quickly anyway and four more that will actually be used in anime.
The main three are san, chan and kun. San is to show respect, whether it's used to refer to someone above me in a hierarchy whom it would be rude to disrespect or to someone equal to me that I just want to respect (like a classmate if I'm not very assertive). When Iwata died a lot of people said to say 'RIP Iwata-san' rather than Mr Iwata.
Chan is to show that you find something endearing or cute, and is basically like adding -y in English, -chen in German or -ka inPost too long. Click here to view the full text.