Give all students a chance to write, even those young enough to not know letters or how to spell words. Even students who make squiggly lings are practicing writing. Whenever a student writes something, ask them to read it to you, and then write the translation underneath so the parent knows what the child was trying to say. These are early writing strategies that encourage students to learn how to write even before they have the knowledge of how to do it.
As students progress, encourage them to write stories using the words that they know. When they don't know how to write a word, they can ask you and you can put it on the board so all students can benefit from it. They should use their best guesses for spelling and again, you can translate the writing so parents and others know what the student is saying and so that the students equate writing with communication.
Students who are capable of writing basic sentences should write in a journal each day. Stress that what they write there is private and won't be shared with other students. Also tell them that they won't be graded on spelling and grammar, because many students get frustrated and anxious when they know they are being graded. This encourages students to simply write and to get into the habit of doing it each day, which leads to good practices in the future.
Older elementary students should practice writing whenever possible. Along with journal time, provide a chance to do writing in each class, even classes like math and science. Writing out math problems in words, and writing out the scientific process that you followed are both good ways to incorporate writing into every class students are in.