This is a big topic.  Conversational verse includes satires, dramatic dialogues, and homey little poems of the Robert Frost type.  To achieve a conversational tone, one has to lower the diction a bit and work somewhat against the metrical rules.  I’m going to stick mostly to iambic pentameter lines.  Let’s start with an example of how it ought not to be done.  Here is an animated scene from Thomas Kyd’s The Spanish Tragedy.  I cite it not to ridicule Kyd or denigrate his deservedly famous (in his lifetime) play, but the generation before Marlow and Shakespeare had not learned (or relearned) how to communicate a lively conversational tone.

[KING.]  Welcome, Don Balthazar!  Welcome nephew!
    And thou, Horatio, thou art welcome too!
    Young prince, although thy fathers hard misdeedes
    In keeping backe the tribute that he owes
    Deserue but euill measure at our hands,
    Yet shalt thou know that Spaine is honorable.

  BALT.  The trespasse that my father made in peace
    Is now controlde by fortune of the warres;
    And cards once dealt, it bootes not aske why so.
    His men are slaine,--a weakening to his realme;
    His colours ceaz'd,--a blot vnto his name;
    His sonne distrest,--a corsiue to his hart;
    These punishments may cleare his late offence.

  KING.  I, Balthazar, if he obserue this truce,
    Our peace will grow the stronger for these warres.
    Meane-while liue thou, though not in libertie,
    Yet free from bearing any seruile yoake;
    For in our hearing thy deserts were great.
    And in our sight thy-selfe art gratious.

  BALT.  And I shall studie to deserue this grace.

  KING.  But tell me,--for their holding makes me doubt:
    To Which of these twaine art thou prisoner?

  LOR.  To me, my liege.

  HOR.                   To me, my soueraigne.

  LOR.  This hand first tooke his courser by the raines.

  HOR.  But first my launce did put him from his horse.

  LOR.  I ceaz'd the weapon and enioyde it first.

  HOR.  But first I forc'd him lay his weapons downe.

  KING. Let goe his arm, vpon my priviledge!

                  Let him goe.

    Say, worthy prince:  to whether didst thou yeeld?
 
Here's a bit of early Marlowe that indicates the poet's interest in having an animated conversation.  It's livelier than Kyd for the most part but not that big an improvement:


MYCETES. Come, my Meander, let us to this gear.
I tell you true, my heart is swoln with wrath
On this same thievish villain Tamburlaine,
And of  that false Cosroe, my traitorous brother.
Would it not grieve a king to be so abus'd,
And have a thousand horsemen ta'en away?
And, which is worse, to have his diadem
Sought for by such scald knaves as love him not?
I think it would:  well, then, by heavens I swear,
Aurora shall not peep out of her doors,
But I will have Cosroe by the head,
And kill proud Tamburlaine with point of sword.
Tell you the rest, Meander:  I have said.


Contrast that with the following scrap from Doctor Faustus:


MEPHIST. That was the cause, but yet per accidens;
For, when we hear one rack the name of God,
Abjure the Scriptures and his Saviour Christ,
We fly, in hope to get his glorious soul;
Nor will we come, unless he use such means
Whereby he is in danger to be damn'd.
Therefore the shortest cut for conjuring
Is stoutly to abjure the Trinity,
And pray devoutly to the prince of hell.

FAUSTUS. So Faustus hath
Already done; and holds this principle,
There is no chief but only Belzebub;
To whom Faustus doth dedicate himself.
This word "damnation" terrifies not him,
For he confounds hell in Elysium:
His ghost be with the old philosophers!
But, leaving these vain trifles of men's souls,
Tell me what is that Lucifer thy lord?

MEPHIST. Arch-regent and commander of all spirits.

FAUSTUS. Was not that Lucifer an angel once?

MEPHIST. Yes, Faustus, and most dearly lov'd of God.

FAUSTUS. How comes it, then, that he is prince of devils?

MEPHIST. O, by aspiring pride and insolence;
For which God threw him from the face of heaven.

FAUSTUS. And what are you that live with Lucifer?

MEPHIST. Unhappy spirits that fell with Lucifer,
Conspir'd against our God with Lucifer,
And are for ever damn'd with Lucifer.

FAUSTUS. Where are you damn'd?

MEPHIST. In hell.

FAUSTUS. How comes it, then, that thou art out of hell?

MEPHIST. Why, this is hell, nor am I out of it:
Think'st thou that I, who saw the face of God,
And tasted the eternal joys of heaven,
Am not tormented with ten thousand hells,
In being depriv'd of everlasting bliss?
O, Faustus, leave these frivolous demands,
Which strike a terror to my fainting soul!


Note the broken lines, and note the way he shapes the rhetorical flow of the speech.