Marvell's narrator uses three methods: humor through hyperbole, fear through imagery of death, and finally, imagery about the fierce pleasures of sex to try to persuade his beloved to make love to him. This a classic carpe diem (seize the day) poem. It is based on the premise that one should enjoy life now, because tomorrow one might die.

The narrator addresses a beloved who apparently is shy or "coy" about making love. He first teases her, saying if he had all the time in the world to woo her, he would gladly spend 200 years praising each breast and 30,000 years on the rest of her body. Unfortunately, he notes, time is speeding along quickly, like a "winged chariot hurrying near." They don't have time, he argues, for all this wooing.

The narrator then turns serious, reminding his beloved that she will die sooner or later (who knows when?) and plays on her fears of death. He pictures her in a vault with worms crawling through her. He notes the grave is not a place of warmth where people embrace. If she doesn't seize love now, she could lose the chance.

Marvell's narrator then turns to the pleasures of sex, imagining how the two of them can outrun time by making love now. He wants them to roll their "sweetness" into "one ball."

Notably, the narrator doesn't address what might have been the woman's greatest fear: getting pregnant in a time when such an event would "ruin" her as far as marriage prospects. He tries to persuade her from his own point of view, but fails to address whether or not he will be there for her if she is "disgraced." He certainly doesn't mention marriage, so we might wonder how persuasive his three points actually are to her.

In Marvell's poem "To His Coy Mistress," the poet uses the carpe diem theme, live for today, for life is fleeting, to attempt to convince his coy mistress to engage in a sexual relationship.

The first stanza is used to tell the mistress of his adoration and her beauty combined with the element of time:

An hundred years should go to praise

Thine eyes, and on thy forehead gaze . . . (13-14)

He compliments different parts of her figure, telling her how many years he would take to adore it. However, at the onset of stanza one, he also tells her that they don't really have enough time for him to worship her as he would like (1-20). Therefore, they don't have enough time for her coyness or shyness.

In the second argument in the second stanza, the tone becomes more dire as the poet uses imagery of death and the grave to try to convince her:

. . . then worms shall try

That long-preserved virginity . . . (27-28)

The grave’s a fine and private place,

But none, I think, do there embrace (31-32)

Here, he stresses how quickly time passes and warns the coy mistress that she could go to her grave a virgin. As well, he warns her that his lust could turn "into ashes." The emphasis in this portion of the argument is literally that their time to become lovers is running out.

The last argument tells the mistress that youth doesn't last forever, and if she becomes his lover, they will have an amazing sexual experience. The poet uses the imagery of "amorous birds of prey" to illustrate the degree of passion that will take place with their coupling. In fact, they will "devour" their time together.

If you wanted to summarize the poem in terms of three arguments, simply put they might be as follows:

1. If we had eternity, there would be nothing wrong with your being coy and not wanting to make love with me.
2. But we don't have eternity, and one cannot make love in the tomb.
3. If we make love now as I want, it will be earth shattering--we will give the sun a run for its money, as they say.

The three "arguments" are organized into stanzas, so they're easy to investigate. 

Of course, the whole is much greater than the sum of its parts.  Reducing this hyperbolic, intelligent, "metaphysical" poem to an essay-like argument does not do it justice.