Start by thinking about the types of characters that move you. Novels or stories you remember, even as far back as high school literature, can give you some ideas. Try to find trends in character traits that appeal to you. Jot down names of books or plays and types of personalities. Keep this around when you search for monologues.
Search for monologues that match your list of character traits, but keep an open mind. Use portions of plays you've performed in or wanted to. Use books, particularly collections of character monologues. Search Amazon.com for books by Glenn Alterman like "Street Talk" and "2 Minutes and Under."
Spend some time writing about the character in the monologue. Begin with a biography. Write a few pages from their journal or have them talk to you about themselves in a letter. It's always a good idea to read the entire play and summarize the situation so that you're not acting out of context.
Practice the monologue in front of a mirror first. Pretend what you're saying is being challenged by someone you know. Respond the way you think the character would. Get another actor to engage in an exchange where you ad-lib a conversation. Be your character and forget yourself.