A metaphor is a comparison that does not use the words "like" or "as." The overarching metaphor in this sonnet is that the speaker's beloved is better than the summer's day they are compared to. In likening the beloved to a summer's day in this novel way, in which the metaphor emphasizes differences rather than samenesses, the speaker is taking a fresh look at the worn-out cliché of comparing a lover to summer's beauties.
A specific metaphor or comparison within the extended metaphor of the beloved as superior to summer is the following:
Sometime too hot the eye of heaven shines
In other words, the comparison of the beloved to a summer's day shows the beloved as better because sometimes the sun (the "eye of heaven") is too hot. This, implicitly, is never the case with the lover.
Likewise, the speaker notes that:
often is his gold complexion dimm'd
In this comparison, the personified sun is shown when he is hidden behind a cloud: summer days are not always beautiful, as the lover always is.
Further, the speaker states:
every fair from fair sometime declines,
By chance or nature’s changing course untrimm'd;
This gets to the heart of the lover's superiority: unlike summer, the beloved's soul is not changeable.
Finally, the speaker notes that the beloved, unlike a summer's transitory day, is immortal because the speaker has written this sonnet, the words of which are "eternal."
In comparing a beloved to a summer's day, the poet is able to highlight the ability of art to confer immortality on a subject.