The following is an example I created of a monologue for the character of… from “Death of a Salesman.”
I am a man who is powerfully made and well built. I have many goals that I want to achieve, but my brother Biff has accomplished more than me. I have been very successful with my job, and have suffered from my father’s expectations, which have pushed me to please my father, but as my father starts to lose his mind, I have focused less on pleasing him and been more self-absorbed. I always live in the shadow of my older brother Biff, who is less self-assured.

This is a monologue because…
It is uninterrupted, and reveals something about the character

This monologue would fit in the current plot when…
When him and Biff were in the bedroom together talking