In many elective courses, your instructor will provide a dataset.
From the papers of George Washington to archives of late nineteenth-century maps, there is online data available in every research area within the discipline. Your first step, then, is locating data that interests you. (Alternatively, you may have already have unique dataset of your own, or your instructor may provide a dataset.)
Remember that data comes in all forms. It can be textual (books, ephemera, letters, manuscripts, newspapers, periodicals, and transcripts), visual (artworks, blueprints, illustrations, maps, photographs, or films), or auditory (music, recordings, and speeches).
If this is your first DH project, you might want to stick to one dataset or type, although there are some rich possibilities when you mix and match. For example, if you are investigating the national response to the Civil Rights Movement, you could gather datasets of American news articles and personal letters between key political figures, and compare the public and private conversations about the Movement. Once you have located your dataset(s), in most cases you should save it in a widely-accepted format (e.g. .csv, .txt, or .xml).