Same as writing any good piece of writing.It needs to be engaging, compelling, interesting and intelligent. There's a huge list of top of that depending on what kind of monologue you want, but really, no matter what the form, good writing is good writing. Obviously you need to be aware of the particular capabilities and limitations of your chosen medium, but the basic rules still apply.
One thing i strive for in such a thing is i like to get the reader thinking. Thinking of anything, i love when they are entertaining and engaging but i like to pose a question and get the reader thinking about the story and what not for hours. I believe as long as it is meaningful your monologue will be good.
the question's too broad to get specific answers... what's it for?... a stand-up comic routine?... stage play or movie script?... something else?
