The best way to go about detecting plagiarism is to be familiar with your students’ abilities. A second way is to read papers carefully when they are submitted. Finally, there are internet services that search the internet to determine if a given paper has plagiarized something that is available online.
Basically, the best way to detect plagiarism is to know what your students are capable of and to read their papers with that in mind. As a teacher, you develop a sense as to what level of writing is within a given student’s abilities. When you get a paper that is clearly beyond those levels, you should suspect plagiarism and take steps to determine if plagiarism has actually happened. Secondly, reading papers carefully is an important step to take. In a paper where the student has plagiarized some ideas or passages, the style and quality of the work tends to be very uneven. A student might write a paragraph in their own style and then follow it up with one that sounds like it came from an academic journal. The student might introduce ideas that you never brought up in class and that have little connection to the subject at hand. All of these are warning signs.