How is time personified?

In Sonnet 19, the poetic persona grants that Time has power over the world and yields to Time's power. "Time" is addressed with a capital {T}, which gives time personification with human attributes, like the power to listen, to negotiate and to act in a decisive manner. It is this personification and these attributes that make the contrasting arguments upon which the sonnet is built.
In the first quatrain (stanza of four lines)--in the rhyme scheme of abab--the persona acquiesces to Time and bows to Time's power to ravage and destroy, as occurs daily, the creatures of earth and mythology:
dull the sharp lion's paw
let earth see the death of and bury her creatures
rot and drop the tiger's fierce teeth
rather than let the phoenix rise to new life from the flames, burn the mythical phoenix that is meant to live forever
In the second quatrain--set in cdcd--the persona acknowledges that Time can create joys or sorrows, and, in short, do anything that strikes Time's fancy. He acknowledges that Time flies swiftly past, destroying all the world's pleasures as it speeds hastily on its way. But the persona dares in line 8 to stand up to Time and forbid one action to Time [later, the persona acknowledges that he has no power over Time, but here, he is assertive].
make seasons of joy or sorrow appear as you fly swiftly, heedlessly by
your power is such that you do whatever you want, you swift running Time
whatever you want, do to the world and all its time-ruined pleasures and beauties
but of all your crimes, there is one I forbid you to do
In the third quatrain--rhyme scheme efef--in which the contrasting argument is introduced, the persona says that makes it forbidden for Time to put a mark of destruction on the beloved to whom the sonnet is dedicated. Time may make no mark, may leave no trace on the youth's beauty.
put no deep lines of passing years on the beautiful forehead
nor put any fine lines there either
let the youth go through time untainted, unmarred, with no diminishment to beauty
do this so that he may be the example, the measure, the gold standard of beauty to all men
The last two lines of the poem, lines 13 and 14, are a couplet--with the rhyme scheme of gg (in the sonnet ababcdcd efefgg rhyme scheme), having "wrong" rhyme with "young"--and these lines resolve the paradox that the contrasting arguments of the sonnet create: The poetic persona wants to control Time and force Time to leave untouched the most beautiful youth he knows. This is a paradox because, while acknowledging Time's swift, all-powerful race to destroy, he demands that Time turn away from one individual.
The resolution to the paradox is two-fold. First, the persona acquiesces and yields to the absolute power of Time: "Yet, do thy worst...." "Yet" is a contrastive conjunction that acknowledges the oppositional nature between the thing that comes first and the thing that comes second: I demand "this," YET I know what will truly happen is "not-this."
Second, the persona claims with more authority and certainty that, regardless of the wrong Time will do to the youth's beauty, "Despite thy wrong," the sonnet will preserve for all ages the testament of the youth's beauty, thus making his beauty immortal, untouched, unravaged by Time and the standard of excellence for all men to be measured by.
That the poet's pen and words renders the subject of the poem immortal, forever living, is a classic poetic convention seen often in Renaissance poetry, particularly in Renaissance sonnets, like this and others of Shakespeare's and in sonnets of Edmund Spenser as well as other sonneteers. The poet's ultimate power over time is the words of the poems, the words that will be read--as are Shakespeare's and Spenser's and others--throughout all ages.
Thus (1) the resolution to the paradox of the metaphor (personification of Time), (2) the resolution of the paradox of the contrasting arguments (acknowledging Time's ultimate power, yet giving Time orders), and (3) the resolution to the paradox of immortalization of beauty is that Shakespeare's sonnet to the youth's beauty is being read now, today, by us, whose attention immortalizes him.