The bane of my existence in teaching is plagiarism. I do everything I can to explain to students why they should not plagiarize, and I spend a significant amount of time on making sure they know what it is. I even have them take a quiz on it before their first big paper. Despite all that, there are always the cheaters.
The luxury of being a writing teacher, however, is that I can usually discourage most of the cheating by requiring a process that would make it difficult to turn in a copied paper. Here is the process that I use (which is also just a good process for writing in general):
1. I ask a specific question, perhaps comparing and contrasting two different articles, or limiting their choice of topic. This makes it harder to find something to copy that fits the prompt. I never assign an open-ended paper.
2. I require students to turn in sources ahead of time for approval. They are free to change their minds about the sources, but they must email me links to their new sources any time before the paper is due. Sometimes, if the topic is narrow enough, I supply one of the sources as a starting point and require that they include it.
3. I assign in-class, graded assignments for the paper. Perhaps students will write two or three introductions and then do group work to determine the best introduction for their papers. Maybe I will have them free write a body paragraph, or turn in a finished paragraph for feedback.
4. I always require a rough draft and rewrites. If they do not turn one in by the deadline, they still have to include one with their final paper, or they don't get any credit.
None of these alone will deter all plagiarism, but taken together, it would be more work to plagiarize the whole process than just writing a new paper.
Most important, however, is early intervention for someone who seems overwhelmed. If a student has been absent a lot and not turning in preliminary assignments or in-class work, I take them aside and ask how I can help, and gently work into the conversation that they must be careful not to panic and do something that they would regret later. In my experience, the students who plagiarize are those who have procrastinated or tried to do a last-minute paper and gave into the temptation to try the easy way out. I tell my classes frequently that anything they can accomplish is far better than anything they can copy.
Here are some resources to help your students understand plagiarism. The first is a free checklist you can use in your classroom and the second is a complete teaching plan with explanations, examples, exercises and a quiz.