Seeming realistic while acting has only been a goal for most actors in the last 50 years or so. Before actors were more worried about how they looked and sounded, than portraying a psychologically real being present on stage or on the screen. Realistic acting monologues revolve around the most simple bodily function that you could think of, one that most humans perform unconsciously- the act of breathing.
I learned this method from Paul Bernstein, and it works. Once you memorize your lines, you will become much less self aware. This is both good and bad, if you are self aware, you can fix mistakes that may come before you ever perform anything. However, many actors feel dread from being self aware, and breathing accentuates this painful self realization of who you are (not yourself) while realistically acting a monologue. If you can handle this state of mind, then congratulations, you have a natural affinity for acting, if you do not, then you may just be doomed to mediocrity when it comes to this art-form. Don’t worry, acting is not something you can just delve into, it’s like learning how to do everything you learned as a child, but only as another person.
After breathing comes voice. No matter what your voice must be different from what it is in real life. I don’t mean taking a voice and putting it into all the characters you do, because I have seen that before and it is quite annoying if you watch that actor in multiple roles. Find an article, or a worksheet or anything on linguistics and learn a little something about how people from different areas pronounce syllables in their certain accents. Accents are not just for stylized interpretations of people from different regions, I feel as if every person has their own unique accent depending on what sounds they have been surrounded by in their life. Examine the little quirks you see around you, in public, stare at people and recognize their unique vocal traits and mouth movements. You will be intrigued.
The most important part of performing realistic acting monologues is presence, whether on stage or in film, how you carry yourself is crucial. Posture is key to levels of status, certainly, but knowing where to make people look at what times, while making everything you do seem not contrived is difficult unless you can relax and be natural. Presence is all about understanding the psychology of your character, not just memorizing blocking (stage movement). You must incorporate improvisation into everything you do, even in a major production where the director demands you don’t deviate from his or her rules, deliberately breathe at a different pace.
Live what you are doing, you don’t necessarily have to believe that you are the character you are portraying, because most of the time “method actors” are lying when they say they become a character. The only way you can perform with method is if you are self aware, so saying you are something you aren’t doesn’t make sense. The art behind acting is building up all of the tiny choices you make and living them in fresh ways that people will enjoy and possibly learn something from. Your audience is the most important thing about acting, and so you must appease them. Modern audiences want realistic acting, and they especially want realism in monologues, so you must give them what they want.