This is a summary of the story:
-Alice sits by her sister but grows bored. She sees a rabbit and gives chase which leads to her falling down the rabbit hole. After landing, she finds she's in a hallway. Then she hears the Rabbit and follows him. She ends up in a little room with doors. There she shrinks and grows while trying to get the key for the smallest door, which leads to the Queen's garden.
-Stressed, she begins to cry. Her tears quickly become a pool. (She is very tall at this moment though) The White Rabbit comes by and Alice says one sentence to the him. Her height scares him off. She picks up his fan and finds shrinks her. She takes a step and falls into the pool of tears.
- In the pool she meets a mouse. They find land. A lot of birds, the mouse, and some crabs want to dry off. To do this they finally decide on a race where everyone wins. After the race, Alice gives everyone a prize. She then scares the animals off by talking about her cat.
- The White Rabbit runs by and mistakes Alice for his house maid. He sends her to fetch him a new pair of gloves. She finds his house and drinks from a bottle in his room. It causes her to grow. She becomes stuck in his house. The W.Rabbit notices and tries to get her out by sending Bill the lizard down the chimney. Then they decide to burn the house. First, they throw pebbles into the house, and the pebbles turn into cake. Alice eats one and shrinks again. She leaves the house and runs into a giant puppy. Afraid, she throws a stick to get rid of it.
-Alice meets a caterpillar. He tells her one side of the mushroom will make her grow, the other side will make her shrink. Experimenting with the mushroom, she grows and runs into a bird who thinks she is a serpent. She leaves the mushroom and comes to the Duchess's house.
- When she finally gets inside, she meets the Duchess, her crying baby, the Cheshire cat, and a cook who uses too much pepper. Alice ends up holding the baby and leaves the house. In the woods she scolds the baby. It turns into a pig. She lets it go and it wanders of into the woods.
- The Cheshire Cat appears and asks what became of the baby. The cat and her talk. Alice wants to know which way to go, the cat tells her it depends on where she wants to go. Alice ends up walking to the March Hare's house where the mad tea party is going on. Alice sits down uninvited. She ends up leaving because of their rudeness.
- She finds a tree with a door in it. Entering the door, she finds herself in Queen's garden. Three cards are painting the roses. The Queen and her party pass. The Queen yells at the cards. Alice is invited to play croquet.
- The game begins. Alice can't figure out how to hold her flamingo. The Cheshire Cat's floating head appears and talks to Alice. The king notices, asks the cat to kiss his hand, and the cat refuses. He calls for his wife and she says 'Off with his head!'. The executioner is sent for. The executioner, King, and Queen argue if the cat can have his head cut off since he is only a head. Alice tells them the cat belongs to the Duchess.
- The Duchess is sent for. Alice and the Duchess talk. The Queen comes and scares the Duchess away. The Queen asks Alice if she's seen the Mock Turtle yet. Alice says no, the Gryphon is sent for, and he takes Alice to the Mock Turtle.
- The Mock Turtle and Gryphon talk to Alice. They perform the lobster quadrille for her. Next, Mock turtle sings for her. The trio leaves for the trial.
- Everyone is in the court room. Alice ends up angering the Queen by speaking freely. The Queen's card soldiers attack Alice, and Alice wakes up with falling leaves landing on her.
- Alice tells her sister about her strange, yet exciting, dream and then runs home. Her sister sits on the bank thinking about the dream and then imagines Alice growing old and telling her children wonderful stories.
What parts are important: I'd say keep the scenes people know about. That would be her falling down the hole, ending up in the room of doors, crying, swimming in her tears, meeting the animals on the bank, going to the White Rabbit's house and getting stuck, meeting the Duchess, talking to the Cheshire Cat in the woods, the mad tea party, the croquet part, the court scene, and Alice waking up.
Hope this helped.