The trick is to make it as much like a two-person show as possible. By which I mean that you (in collaboration with the actor) need to figure out who the actor is talking to: is it the audience? an imaginary other character on stage? himself?
"Himself" is the hardest, but it's doable. In this case, the actor needs to come up with two characters -- the one who is talking and the other part of himself that's the listener. This sounds schitzo, but we do it all the time. If you've ever had to "talk yourself into something," you know what I mean.
Why do we need this second character? So that the actor can go into Stanislavsky mode -- so that he can have an action he's trying to play against the other character. He needs to be trying to win something from the other character -- from the audience, the imaginary person on stage or some other part of himself. This is the way actors are taught to work, and this is the way they work best.
Note: if you're confused about this "Stanislavsky stuff," please see http://wscmonster.blogspot.com/2011/04/how-to-direct-plays.html (scroll down to the section called "focus on the characters and what they're trying to achieve.")
Once the actor has chosen his scene partner, I urge him to create an adversarial relationship between himself and that partner. I don't mean they have to be bitter enemies (though that's an acceptable choice). They just can't be on-the-same-page about the topic-at-hand.
(I always think of the Cowardly Lion saying, "I DO believe in spooks! I DO believe in spooks! I DO! I DO! I DO!" Who is he trying to convince? I don't know, but he's going at it like gangbusters! It must be someone who is adamantly saying, You DON'T believe in spooks!")
Let's say we've decided that the other character is the audience. If the scene is a speech in which the actor makes a plea for "peace in our time," there's no reason for him to work very hard if he's speaking to a bunch of pacifists. So, regardless of the truth of the audience's mindset, the actor should pretend that he's in front of a bunch of warmongers. And he has this one speech to change their minds!
If the actors is "talking to himself," and the speech is about "how I really need to go on a diet," then the other-self he's talking to needs to be of the opinion that diets are a waste of time -- "sure, you'll lose weight, but you'll be unhappy. And then you'll just start eating again and you'll gain the weight right back!" The actor need to use his speech to conquer that attitude in himself!
Once we figure all that out and the actor gives it a try, it's usually works pretty well, but there are a lot of nuances that aren't all that interesting -- that the actor tends to gloss over or play on one note.
So I usually work with him to break the scene down into a dialogue instead of a monologue, making up what the audience -- or the other-self -- might say. For instance, the chorus (usually played by a single actor) in Shakespeare's "Henry V" has a problem. He wants to tell a grand story of kings and princes and war and glory, but all he has is an empty theatre and a few actors. He has to walk in front of an audience that (we're pretenting) is expecting to see a Spielberg movie, with epic battle scenes and expensive period costumes...
O for a Muse of fire, that would ascend
The brightest heaven of invention,
A kingdom for a stage, princes to act
And monarchs to behold the swelling scene!
Then should the warlike Harry, like himself,
Assume the port of Mars; and at his heels,
Leash'd in like hounds, should famine, sword and fire
Crouch for employment.
For those of you who are a little rusty with Shakespeare, he's saying "Oh, I wish I had a muse of fire -- some magical god of the theatre who could help me out by coming up with all sorts of amazing effects! I wish I had an actual kingdom here instead of a stage, and actual princes to act in my play (instead of this motley crew of actors). And instead of you -- a ragtag audience -- I wish we were playing before a royal court! IF I had all that, then the warrior-prince Harry (the hero of my story) would seem like the God of War, which is how he seemed in real life!
So we might start this way:
Audience: Hey, I paid to see something like "Platoon" or "Full Metal Jacket!" Instead I get THIS? An bunch of old farts prancing around the stage in cardboard armor? Are you KIDDING me? You're the storyteller! What are you going to do about it?
Chorus: Oh, for a Must of fire, that would ascend the brightest heaven of invention!
Audience: Oh, come on! That wouldn't be enough to help you. You'd also need...
Chorus: A kingdom for a a stage!
Audience: A kingdom populated by a bunch of effeminate ahk-tahs? Don't make me laugh!
Chorus: Princes to act!
Audience: Good look with that. Where's the exit?
Chorus: And monarchs to behold the swelling scene!
Audience: Hey! We're not good enough for you? You think if a bunch of kings and queens were watching your play, it would be any better?
Chorus: Then should the warlike Harry, like himself, assume the port of Mars, and at his hees, leash'd in like hounds, should famine, sword and fire crouch for employment!
I often take on the role of the audience (or other self) and perform the scene a few times with the actor, as if it's a dialog. This allows me to say, "Wait! You can't move unto your next like yet. You haven't convinced me of your last point."
(Remember to talk in terms of specific tactics: "chastise the audience ... not tease them ... now shame them ... now flirt with them ... now flee from them ... now lunch at them ... now argue with them as if you're a lawyer, making your final argument before the supreme court ... now belittle them ... now invite them to join you in celebrating ... now utterly reject them...")
Once the scene works as a dialog, I pull the audience's lines out and ask the actor to play the scene again, this time just imaging what the audience is saying.
Note: sometimes you don't have to make up an audience that is THAT confrontational. If the actor is making some kind of argument in his speech, it might be enough to say, "They're friendly, but they're not convinced you're right. Convince them!" But if the actor is boring, you may have to raise the stakes: "they don't agree with you, and they have a meeting in five minutes. So if you're going to convince them, do it now and make it snappy!"
ALWAYS remember the stakes! If the actor is doing his work -- you can see he's trying to convince the audience -- but he's just not THROWING HIMSELF INTO THE TASK AS IF HIS LIFE DEPENDS ON IT, it may mean the stakes are too low for him: "I think the stakes are a little low here. You're trying to convince the audience that you didn't steal the money. But the think is, you can see some of them on their cellphones. They're dialing 911. They're calling the POLICE! You need to convince them NOW or you're going to JAIL!"
In some speeches -- especially in Shakespeare -- the fun for the audience is being let in on a character's thought process. The key word here is PROCESS. They don't want a report of something the character has already figured out. They want to see him, in real time, grapple with a problem, get stymied, get frustrated, get an idea, come to a solution.... They want to be there and witness the exact moment the lightbulb goes on in the actor's eyes.
Below is another dialogue I might use in rehearsal, to help the actor "argue with himself," as his character grapples with a problem.
As an example, here's the beginning of Hamlet's most famous soliloquy. I've split him into Hamlet1 and Hamlet 2. For the most part, Hamlet 1 says lines I've made up and Hamlet 2 is the "real" Hamlet, the one the audience will actually meet. But, as you'll see, I've given a few of Shakespeare's lines to Hamlet 1, indicating that, sometimes, the audience really sees a schizoid slip in real time.
Again, I would perform this with the actor, gradually letting him own both parts, gradually making most of the Hamlet 1 lines occur silently, just in the actor's head.
Hamlet 1 : you're clearly troubled by something. What is it?
[Hamlet 2 can't answer right away. He squeezes his eyes shut, thinks REALLY hard .... and AH HA!]
Hamlet 2: To be, or not to be: THAT is the question:
Hamlet 1: I don't understand. What are the two options, exactly?
Hamlet 2: Whether 'tis nobler in the mind to suffer the slings and arrows of outrageous fortune...
Hamlet 1: OR...? Or WHAT?
Hamlet 2: Or ... [It occurs to him! Ah! ] ...to take arms against a sea of troubles, and by opposing end them.
Hamlet 1: I don't get it. What would be the payoff for THAT?
Hamlet 2: [As if talking to a small, stupid child ] To die: to sleep; No more;
Hamlet 1: Just go to sleep? Isn't that just avoiding the problem?
Hamlet 2: [pausing to figure out how to explain this.... Ah!] and by a sleep to say we end the heart-ache and the thousand natural shocks that flesh is heir to...
Hamlet 1: I still don't get it.
Hamlet 2: [Coming up with the perfect way to explain his point] 'tis a consummation Devoutly to be wish'd. To die, to sleep; To sleep: perchance to dream:
Hamlet 1: ay, there's the rub; For in that sleep of death what dreams may come when we have shuffled off this mortal coil!
Hamlet 2: [Oh, shit! You're right.... that] must give us pause...