This is an experimental site. I try to split up the first episode into acts, sequences, scenes, and shots (as Wikipedia suggests) to make it easier for everyone to find the right point for inserting new text.
Title: Cocoon - A Dream of Falling from the Sky - Old Home
A girl dreams of falling from the sky before she hatches from a cocoon. A group of five haibane welcomes her as she wakes up in the Guest room of Old Home. After telling them about her dream, she is named "Rakka" (by Reki) and presented with a halo (by Hikari). When all others but Reki leave, she painfully grows her wings. After the fever is gone, she can stands up.
For a more detailed summary, read about Episode 1 on Sekai no Hajimari.