Stress the importance of clear, thoughtful writing. In general, faculty who tell students that good writing will be rewarded and poor writing will be penalized receive better essays than instructors who don't make such demands. In the syllabus, on the first day of class, and throughout the term, remind students that they must make their best efforts in expressing themselves on paper. Back up your statements with comments on early assignments that show you really mean it, and students will respond. Regularly assign brief writing exercises in your classes.
Writing is a complex set of skills that requires continuous practice.
You need not assign weekly papers to give students experience in writing. To vary the pace of a lecture course, ask students to write for a few minutes during class. Provide guidance throughout the writing process. After you have made an assignment, discuss the value of outlines and notes, explain how to select and narrow a topic, and critique first drafts. Don't feel as though you have to read and grade every piece of your students' writing.