I hear too many people saying "I hate anime
", "Do you like anime?", or "Yeh I'm really into anime". Stop the madness!
When was the last time you heard someone say "I really hate films", or "I'm really into this music
Anime is not a genre
It's like saying foreign films are a genre, which is silly. Of course some people don't like watching foreign films (shame on them), and some people don't like watching anime, but that's usually because they aren't used to it or have some sort of pre-concieved notion about it (which is usually false).
Here's what to do with anime, and any film at all really:
Watch it like it's any other film.
Forget about the whole anime scene, the cosplay, the fanart, the fanfics, and all that rubbish. The whole beauty of animation is that anything is possible, there are no rules, so all this nonsense about anime always having characters with stupid hair, or big eyes is not true. In fact there are some great films that people are missing because they dismiss them as anime. Watch films like Perfect Blue, Grave of the Fireflies, Ghost in the Shell, or Princess Mononoke without caring about this whole anime fanbase stuff, and don't worry if you think you don't think you understand anime because they're just films.
Although having said that, any film is a product of the culture it comes from just like all art in some way reflects the time it was made. But all that means is that you might not get some of the japanese cultural references, it's not the same thing as not "getting" anime. Anyway, most so-called "otaku's" probably don't get them either.
Oh, and one more thing. Try to avoid watching anime with anime fans. If you do you'll have to put up with them talking through the film, with comments like "oh that bit's done differently in the manga", "hey, that's sooo like that bit in (insert random anime series you've never heard of here)", "Asuka!!! (or any character name) Oh s/he's so cool!", or "well if you don't get the story, just admire the animation". They will also tell you to be quiet because "this is a really good scene/ this bit's amazing/ something really important is about to happen", despite having conversations with each other throughout the film about stuff that happens later on, because they've seen it several times and know the plot inside out.