This is kind of a complicated question. (My bona fides: I’ve been acting for twenty years, I have a BFA in the subject, I’ve read all of Shakespeare except Two Noble Kinsmen and Rape of Lucrece, I’ve done a whole bunch of classical plays, blah blah blah.)
Bounded by a nutshell, the idea behind modern interpretation is this: Use the structure of the verse to analyze the organization and expression of a character’s thoughts, but speak those thoughts as clearly as possible for the audience.
Here’s an example, using the first four lines of Romeo and Juliet because we all pretty much know them. Warning: somewhat technical textual analysis follows.
Two households, both alike in dignity
In fair Verona, where we lay our scene,
From ancient grudge break to new mutiny,
Where civil blood makes civil hands unclean.
Simplified and reworked, with subordinate clauses removed, the basic thought here is this: “Two households break from ancient grudge to new mutiny.” That thought is captured in one sentence that, with supporting clauses, spreads over four ten-syllable lines. The actor speaking these lines needs to consider why that sentence is organized the way it is, why the pieces of the thought are broken into these lines, and how to deliver the sentence so both the sense and the implications are conveyed to the audience.
First basic principle: the last word in each line is significant.
Dignity — scene — mutiny — unclean. Positive word, acknowledgement of theatricality, and two harsh words. The first sentence of the play captures and establishes the overall direction of the story to follow. The actor begins to construct a road map for the speech, using this information.
Second basic principle: the pentameter is consistent.
Iambic pentameter is made out of five two-syllable feet. Each foot is called an iamb, and rhythmically goes “ba-DUP.” Five of them together make one ten-syllable line, which is the conventional pattern in this style of verse. However, Shakespeare will regularly add one or two syllables to a line, or occasionally subtract one. “To be or not to be, that is the question” has eleven syllables, which tells the actor something about the actor’s state of mind. The four lines we’re examining here, by contrast, are all regular ten-syllable lines.
Third basic principle: the iambs are irregular.
The pattern of iambic pentameter is “ba-DUP ba-DUP ba-DUP ba-DUP ba-DUP.” That doesn’t mean every line needs to be spoken with that rhythm; it can sound inappropriate and unnatural. This, for example, is just silly:
Two house-holds, both a-like in dig-ni-ty
Sometimes, however, that can be the proper rhythm, as in the first line from Merchant of Venice:
In truth I know not why I am so sad
Of course, the actor playing Antonio may choose to deliver the line differently if he wishes:
In truth I know not why I am so sad
The two choices communicate different states of mind. If you’re going with the rhythm, you may decide it’s because Antonio is speaking casually, brushing off his friend’s inquiries. If you go against the rhythm, you may decide Antonio is more agitated, and more argumentative. Evaluating the rhythmic choice in the context of the verse structure helps guide the actor to these emotional beats.
Returning to our four lines, let’s take a stab at identifying the rhythm of the first one:
Two house-holds, both a-like in dig-nity
Six stresses, rather than five, with three in a row at the very top. Makes sense, given that it’s the first line of the play, and the actor delivering the prologue wants to grab the audience immediately, and focus their attention.
The third line has a similar rhythmic deviation:
From ancient grudge break to new mutiny
The standard iambic beats make no sense:
From an-cient grudge break to new mu-ti-ny
This is a better choice:
From an-cient grudge break to new mu-tiny
Two pairs of neighboring strong stresses. The word “break” breaks the rhythm, and therefore deserves an extra bit of emphasis. “New” also falls on what would otherwise be a weak syllable, and likewise warrants further stress.
Fourth basic principle: consider the vowels.
When speaking classical verse, the consonants generally act as punctuation, while the vowels carry the language and most of the emotion. The vowels in our first line are, in order:
oo - ow - oh - oh - uh - eye - ih - ih - ih - ee
Rather a clear progression, going from big booming roundness to thinner, crisper sounds. Again, a sensibly organized line, grabbing the audience’s ears at the top and leading them along into something a little more particular and delicate. We’re launching into a long-ish sentence, so we want to prepare the audience for parsing the thought to follow.
Fifth basic principle: syntax and logical structure.
This is about how the various thoughts are organized, ordered, set in progression or against one another. Consideration of line-by-line division really helps here.
Two households, both alike in dignity
In fair Verona where we lay our scene
Two lines to establish the setting. One gives us the organizing principle by which we will understand the characters’ relationships, i.e. two families with equivalence in nobility; the other introduces the place. Each gets its own line.
From ancient grudge break to new mutiny,
Where civil blood makes civil hands unclean.
The conflict of the play is here introduced. In doing so, Shakespeare employs a rhetorical device, setting one idea against a second, contrasting one thought against another, to introduce both the plot and its underlying themes. Two households, the Capulets and Montagues, will be fighting against one another, and Shakespeare begins the this-versus-that comparisons immediately. “Ancient” contrasts with “new,” and “grudge” leads to “mutiny.” “Civil” is used twice, paired with two different words, “blood” and “hands.” Back and forth. One against the other. And remember what we saw above, how “grudge break” and “new mu-” represent a double pairing of strong stresses. Additional evidence that that rhythmic choice is the correct one.
So look at the opening sentence again:
Two households, both alike in dignity
In fair Verona, where we lay our scene,
From ancient grudge break to new mutiny,
Where civil blood makes civil hands unclean.
Four different thoughts, the first two closely related, the second two also related. The first two tell us where we are, the second two tell us what’s going to happen. Both the rhythm and the logical syntax tell us that the exposition of the first two lines gives way to action and conflict in the second two lines. The words that end each line are thematically important because of their position, and doubly important because of the rhyme. However, the complete sentence spans all four lines, and the actor must deliver the full thought in a sensible manner in order to communicate all of this information to the audience.
Note that the audience may or may not get all of this detail. The antithetical elements probably won’t be consciously recognized, but as long as the actor recognizes the syntax, and knows why it’s there and how it helps organize the thoughts and themes, the audience will get it on some level.
Now. This is an obvious example. I mentioned “to be or not to be” above. Look at the first few lines:
To be or not to be, that is the question; (eleven syllables)
Whether 'tis nobler in the mind to suffer (eleven syllables)
The slings and arrows of outrageous fortune (eleven syllables)
Or to take arms against a sea of troubles, (eleven syllables)
And by opposing end them? To die: to sleep; (eleven syllables)
No more; and by a sleep to say we end (ten syllables)
The heart-ache and the thousand natural shocks (ten, or eleven, depending on “natural”)
That flesh is heir to, 'tis a consummation (ten syllables)
Devoutly to be wish’d. To die, to sleep… (ten syllables)
Typically, in Shakespeare, when somebody is regularly running over the ten-syllable limit, it means their thoughts are tumbling out, that what’s going on in their mind is rushing ahead of their words, that they have more to say than they can comfortably manage in a well-ordered rhythmic structure. That’s definitely true for Hamlet, all the way through the play. In addition, in contrast to the Romeo and Juliet prologue above, thoughts and sentences are not discretely captured within lines; sentences end in mid-line and new thoughts pick up immediately. The verse, obviously, is telling you something significant about what’s going on with the character.
Consider the sixth line:
No more; and by a sleep to say we end
It’s the first ten-syllable line after five eleven-syllable lines, and the last word in the line is “end.” The speech is about a lot of things, but endings, especially death, are central in the imagery. It cannot therefore be an accident that the word “end” has such prominence, given the structure of the verse, and this implies to me that the word hits Hamlet fairly strongly at that moment, giving him perhaps a pause after the tumbling rush of the first five lines, a moment of internal response, before he continues with the rest of the speech. And that, obviously, is an acting choice that comes directly out of consideration of the verse.
The general point is, while different productions and different directors may want the verse to be delivered in different ways, the responsible actor will always keep it mind. The dialogue needs to make sense for the audience, but there is a ton of stuff that the actor can pull out of the verse to untangle the character’s state of mind, in order to make choice about what sense is to be made to the audience. Line breaks are quite significant, in the context of syllabic and rhythmic analysis, but they’re just one of a dozen things the actor needs to keep in mind.
I could talk about this stuff all day. Let me know if there’s a particular speech or line you want to discuss.
Okay, saw the new thought on preview. Given what you’re trying to do — it depends. If based on an evaluation of the verse, the sense you want to communicate would be lost by running the line together (c.f. the “to be or not to be” speech above), then preserving the line breaks is important. If your excerpt takes the thought out of context, or if you decide based on your analysis that the line break is not significant for your particular usage, then don’t worry about it.
The key thing is that the verse is not a blueprint — it’s not a rigid set of instructions that requires every actor deliver the verse the same way. Rather, it’s like a map, combined with a bunch of signposts and landmarks. Most actors who follow the path will take more or less the same route, but there’s no reason an adventurous interpreter can’t choose to crash through the bushes every now and again.