Section I (Lines 1-8) Summary

Get out the microscope, because we’re going through this poem line-by-line.

My mistress' eyes are nothing like the sun;

Here we are introduced for the first time to the main character in this poem, the speaker's "mistress."
Today, when we use the word "mistress," it's usually to refer to a woman who is dating a married man. In Shakespeare, though, it was more general, like "my love" or "my darling."
The speaker jumps right into his anti-love poem, letting us know that this lady's eyes aren't like the sun. Well, so what? We wouldn't really expect them to be, would we?
As we read the next few lines though, we see that the comparison is a standard way of praising a beautiful woman in a poem. It's like saying, "her eyes are like sapphires."
Our speaker is refusing to fall back on clichés though, instead telling us that this simile doesn't apply at all.

Coral is far more red than her lips' red;

If you imagined a stereotypically beautiful woman, like a model in a magazine, she'd probably have red lips, right?
Certain kinds of very red coral are polished and used to make jewelry so if you compared lips to coral, you'd be thinking of the most beautiful, shiny red thing you could imagine.
Nope, says the speaker, that doesn't sound like my girlfriend's lips at all.

If snow be white, why then her breasts are dun;

Next come the mistress's breasts.
They get pretty much the same treatment as her lips.
If the reddest red is like coral, then the whitest white is the color of snow. A poet could praise a woman for having skin as white as snow.
Not here, though. This woman's skin isn't white, or even cream colored. Instead, the speaker calls it "dun," a sort of grayish-brown color.
Be sure to notice the little changes here. In the first two lines, we hear only that the woman isn't like these other things (the sun, coral).
Now we get an actual description, an adjective ("dun") that applies to her. Unfortunately, it just makes her sound uglier. Dun is a word often used to describe the color of a horse, and definitely not the kind of thing a woman would be thrilled to hear about her breasts.

If hairs be wires, black wires grow on her head.

Now things just get worse.
If a poet wanted to be sentimental and sweet, he might compare his lover's hair to something soft, smooth, and shiny, like silk. Here though, the mistress's hair is compared to black wires sticking out of the top of her head.
Keep in mind that the whole point of this poem is to push back against standard ways of talking about women in poems. So it's not necessarily bad that she has frizzy black hair.

I have seen roses damasked, red and white,
But no such roses see I in her cheeks;

There's a tricky word here: damasked. Basically it just means a pattern of mixed colors woven into expensive fabric.
So imagine a rose with a white and red pattern on it, or maybe a bouquet of red and white roses. Our speaker has seen beautiful roses like that, but his mistress's cheeks don't remind him of them at all.
Maybe some perfectly beautiful woman has cheeks that are white with just a little blush of red, but that's not the woman he's talking about.

And in some perfumes is there more delight
Than in the breath that from my mistress reeks.

By now we've got the idea, right?
The speaker tells us that some perfumes smell better (give more "delight") than this woman's lover's breath.
Apparently she stinks, too.
Let's recap quickly: so far the speaker said that his mistress's eyes aren't that great, that her lips aren't that red, that her skin is yellowish, that her hair is like wires, that her cheeks are nothing like roses, and that her breath reeks.
What a way to start a love poem.