Read some classic comedy monologues to get an idea of what these great writers achieved with these monologues. Many plays by William Shakespeare, George Bernard Shaw and Neil Simon have comedic monologues contained within.
Think of a topic or situation that would create tension and provide you with an opportunity to deliver a monologue. For instance, your character could be breaking up with a long-term partner or firing someone from a job. Confessions often are delivered in monologues and could be used in many different situations. Don't be afraid to choose a serious, tough or sad situation or topic for your monologue. This tension between the subject matter and the comedic performance can provide great comic relief.
Create your character. This character can be someone similar to you or based on someone you know. You will have little time to develop this character in a monologue, so choose character traits that are strong and often conflicted. For instance, a person who often is quick to anger, but cherishes peace.
Think about how your character would act in the situation you've created for the monologue. Think about your character's objective in the situation and what he or she would like to achieve by giving the monologue. If it helps, write a short background story about the character's past and what happens to the character after she gives the monologue. Draw from these stories to create a relatable character.
Practice speaking in the character's voice. Tape record this is if it helps you. Use a lot of movement when becoming the character. Physical movement will help you move the monologue along and keep up the energy level.
Imagine a situation that happens in the middle of the monologue that could change the course of the speech. Maybe someone else enters the room, or the character becomes distracted by something happening outside. Think of how this would affect the character in the scene.
Use these elements to begin writing your monologue. Try to keep up the energy level and vary the emotional tone and comedy of the piece in order to keep your audience interested and showcase your ability as an actor.