Listen for conversations on buses, on the street, in restaurants--anywhere you happen to be--to use as fuel for your monologue writings. Pay attention to how real people speak and react to one another in everyday life. Observe others' body language to use as stage directions in your monologue.
Watch plays and films of all genres and listen for monologues. Take special note of the beats (changes of a character's state of mind, motivation or view of other characters) in the monologues you see.
Read other published monologues--and particularly the classics, like Hamlet's soliloquy--to ensure thorough knowledge of the monologue tradition.
Write without editing your thoughts. Start by creating a life for the character, including personality traits, where she lives, who her family and friends are and what her wants and needs are.
Read your monologue aloud to hear how it sounds. Place varying emphasis on phrases each time you read it to hear how it changes the meaning.
Use one of many online self-publishing resources, such as Lulu.com, Trafford.com or CafePress.com, to distribute your monologue to a wide audience (see Resources below).
Send your monologue or collection of monologues to self-publishing houses. Expect to pay a moderate fee for publication if they accept your work.
Submit your monologue to a theater magazine for publication. Either submit online or by snail mail with a self-addressed, stamped return envelope for an easy response.
Start a blog and publish your monologue on it for others to read and perform.