The story of the animated film is similar to that of the first book, but contains parts of the second book. Dozy Alice is so silly she follows trouble by chasing a talking rabbit down hs hole. At the bottom, she drinks an unknown substance which helps her get through a talking door into Wonderland. Here she meets the Dodo, TweedleDum and TweedleDee (who tell her the story of the Walrus and the Carpenter), the Talking flowers (watch out for the snobby Iris!), the Caterpillar and the Cheshire Cat. She even has un-birthday tea with the Mad Hatter and the March Hare. However, Alice gets caught up in a game of croquet with the Queen of Hearts, and later a trial. The whole thing becomes such a nightmare, Alice realises she's had a dream while she dozed off.
Firstly, I don't know why loads of people think this film is cheesy. I know Alice isn't for everyone, but when you look at the other films made based on Children's classics by Disney (eg- Jungle Book, Hunchback of Notre Dame), you'll see it's more faithful than those films to the original. However if you have read the books and haven't seen this film, some characters are missing (eg- Duchess, Mock Turtle, Knave of Hearts, White Knight). This may just think that Disney has ruined this classic forever. They haven't. It's the best adaption I've ever seen.
Although I actually have the PAL version, I suppose the movie is just the same over in North America. The best bits are the Walrus and the Carpenter, the garden of singing flowers and flamingo croquet. And the Mad Tea Party is still the funniest part of a Disney classic. So buy this movie. Wether it's a video tape or DVD.