Because a dramatic monologue is by definition a single person's speech, it is offered without overt analysis or commentary, placing emphasis on subjective qualities that are left to the audience to interpret. This fact makes the writing of dramatic monologues an exercise in revealing and witholding information, in imagining and communicating experiences, and in being true the the voice of the poem—which is not the voice of the poet.
Some examples of dramatic monologues, also called "persona poems," take on the specific perspectives of real life people. Examples range from poems depicting events through the eyes of historical figures to extraordinary rants made by ordinary people.
In the poem "Mummy of a Lady Named Jemutesonekh, XXI Dynasty," Thomas James lyrically describes the experience of being mummified while witholding the details surrounding the character's death; In "Ludwig Van Beethoven's Return to Vienna, Rita Dove conveys with humor and insight both the passions and paranoias of the famous musician; and in "Falling," the poet and novelist James Dickey describes, almost in real time, the thoughts of a 29-year-old stewardess as she falls to her death after a freak accident.
Choose a biographical figure, famous or not, and write a poem from their unique perspective. Be careful not to offer your own commentary, and instead explore the inner life of the individual. If it is helpful, select a pivotal moment in the person's life and plan to let the poem end there.