Writing assignments for university seem more intimidating than assignments for high school: collegiate assignments are centered around academic writing, which has its own guidelines. If you're wondering about general writing requirements for college, please see What is an Academic Paper? at Dartmouth's Institute for Writing & Rhetoric webpage.
Useful Readings, Sites, and Handouts:
So You've Got a Writing Assignment. Now What? by Corrine E. Hinton, from Writing Spaces: Readings on Writing, Volume 1, 2010
Santa Barbara City College Writing Center's Key Terms: Understanding Verbs Used in Assignments handout
Harvard Writing Center's Tips on Moving from Assignment to Topic
Harvard Writing Center's How to Read an Assignment