Check the student's work to see if it's uneven. If previous work has a different tone or if the writing style is inconsistent and some phrases stand out as being more sophisticated, these can be red flags.
Review the citations and references. If there are few or no quotations or references in a well-written paper, this is another potential sign of plagiarism.
Unusual formatting can also be a clue. Notice if the subheadings are inconsistent, if there is strange usage of upper- and lowercase, or if the formatting or content does not generally meet the assignment requirements.
Search the Internet using one of the suspicious phrases, putting quotes around the phrase. If nothing turns up, try searching for a few more phrases in the student's essay.
Use plagiarism detection software. The Essay Verification Engine (EVE) can be downloaded for $30. TurnItIn is another plagiarism detection program with pricing based on department and campus licensing. WCopyFind is a free program that isn't as comprehensive.