It undermines the whole trust relationship between the teacher and his or her class. Secondly, when essay topics are generic in nature, there seems to be more opportunity to cheat. Conversely, when a paper suddenly appears with no documented process, then teachers should be wary. Lastly, if there are regular in-class writing assignments, a teacher can come to know the students' writing style. Lastly, teachers might want to familiarize themselves with the major web sites which offer papers to students for a fee.
Plagiarism seems so much harder to spot when students only have to cut and paste materials.
I suspect the teachers reading this might offer many worthwhile tips. To me, however, the best way is to simply know the student's writing style. At times we have even asked the student's previous teacher to help us to determine whether the paper or a section of a paper was consistent with the student's work from the previous year. The difficulty comes when you're convinced that something isn't quite right and the student denies any wrongdoing. Different schools will handle this situation in different ways.