Choose a term that is not easily defined; more ambiguous terms are best for this kind of essay. However, you should avoid terms and arguments that have a religious overtone as you cannot be certain that your actual audience will share your beliefs.
Narrow the term to a particular type or situation. For instance, if you were going to define love, you might narrow to platonic love or romantic love, but you would not want to write about both in the same paper.
Decide on your own definition. DO NOT LOOK UP THE DEFINITION IN THE DICTIONARY.
Now comes the tricky part. If most reasonable people would agree with your definition, you wont be able to persuade the readers. In other words, your definition must have a purpose, and if that purpose is already agreed upon, then there is no point in writing about it. For instance, if you were defining digital media, but you were not saying anything new about what digital media is, then that paper would have no purpose. However, if you were defining liberty, and you pointed out that liberty is not the same thing as freedom or justice as many people think, then you would have clearer purpose for your writing.
Once you know what your term is, your intended audience, and your purpose, you can start writing your thesis statement. For instance, if you were to define academia, your thesis might be one that expands the definition: Though many people who consider themselves academics are often defined as such by their position in a college or university, true academia is a process of growing and learning, and as such it must reach beyond the ivory tower of colleges and universities if it is to survive.
Finally, you can start thinking about how you will support this thesis statement. What points will you make to prove your definition correct? Will you use negation? Comparison-contrast?

Its a persuasive definition essay.