I am writing a ten-page children's book based on Twelfth Night from the perspective of one of its characters. Even a start to this task would be very very helpful!

Twelfth Night isn't a complicated story, but there are a lot of ways you can approach the play. In my mind, the obvious choice is to look at this from Viola's point of view. Her desire to find her brother is something that most children will relate to and the fact that she dresses like a boy and gets a job working for Duke Orsino should be entertaining to children. The love triangle may be too complicated for children, but the story is ultimately about Viola finding Sebastian.
Starting a project is always the hardest step. If you reread the play and highlight what you consider the best parts you will have a much clearer idea of what the most important story will be. The first draft is never perfect, but you need something to get you started even if it is just a rough outline.
Children's books should always be lighthearted and fun, so have fun with the project. A comedy like Twelfth Night will make an excellent story.

The first step you should take is choosing a character. One of the interesting things about this assignment is that it forces you to think about how the audience sees things that not every character would know, and thus this assignment will be radically different from a straightforward summary from the viewpoint of an omniscient narrator. Although the obvious choice of viewpoint character would be Viola, it might be more creative to chose Maria, who could give the perspective of a servant rather than an aristocrat.
Maria would not know that Viola is a woman at the start of the play, but she would be privy to Olivia's thoughts and most of the gossip surrounding the court. She could start by introducing the household and her role in it with a witty appraisal of the characters surrounding Olivia. She could talk of Viola's arrival and of what she thinks of Olivia's marriage prospects and how those might affect the household. She might also discuss in some detail her feud with Malvolio and how much she finds Sir Toby Belch entertaining. This probably should be written in the first person and begin with a hook—for example,

While everyone at court is talking about the marriages of Olivia and Viola, the marriage of a servant like myself gets far less attention. From my point of view, though, the marriage of Maria (me!) to Sir Toby is just as important and far more fun. Our story, though, starts not with the marriages, but with the courtships.