For kindergarten students who are just getting started with writing, working with a teacher who reads aloud to students can help get things moving. Read a paragraph or two from a book to students and then let them take turns telling you what they just heard. This gets the kids started in understanding how to tell a story. They can then write a story of their own about a day in kindergarten.
Writing in a journal is an exercise even the youngest of students can take part in. Have students write in a daily journal while in class, jotting down some of the things that happened that day in school. At the end of the week, go over the journal entries with each child, helping each child determine whether anything that was written in the journal could be expanded into a story.
Character cubes are paper cubes you make yourself, with different words printed on each side. Students can roll the cubes to get some ideas on what type of story to write. For instance, a student can roll a set of dice and have it land on words like "princess" and "astronaut." The student can then write a story about the day the kindergarten teacher was sick and sent in an astronaut and princess to substitute.
A kindergarten student can use his imagination to get a story started. Have your class go outside and look up at the clouds, letting students pick one cloud each. The kids can decide what animal or object their cloud looks like, then use that image as a jumping-off point to write a story about kindergarten. For example, if one child saw a dragon in the clouds, she could write a story about the day a dragon came to recess.