Visit an online monologue database such as NotMyShoes.net, UpStageReview.org or MonologueArchive.com to start your search (see Resources below). It's smart to test out the selections on several sites before choosing your piece.
Select your search criteria. Most databases will organize monologues by tone and character type. Options might include comic, tragic or dramatic speeches, as well as monologues spoken by children, men, women or senior characters.
Search by playwright name. If you're already aware of a writer who produces plays you enjoy, this is a good place to start.
Look at writers like Anton Chekhov, Christopher Marlowe, Moliere--and, of course, Shakespeare--if you're seeking a traditional monologue. These works are all in the public domain, so you're likely to find the entire text posted in the monologue database.
Select a more modern monologue by searching plays from the likes of Eugene Ionesco, Samuel Beckett, Bertolt Brecht, Arthur Miller, Tennessee Williams and Edward Albee.
Choose monologues from contemporary playwrights like David Mamet, Tom Stoppard, Suzan-Lori Parks and Wendy Wasserstein to demonstrate your knowledge of recent drama.
Feel free to select monologues from little-known or unknown playwrights, but keep in mind that some monologue databases are open for anyone to post work. If you choose one of these, it's a good idea to have your acting coach or a knowledgeable friend read your monologue selection in order to get a second opinion on its quality.
Obtain a copy of the entire play in which your chosen monologue appears. In order to perform it convincingly, you'll need to read the whole thing so you have a good grasp of your character's inner life and motivations.