Quatrain 1 Summary

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

Thou blind fool, Love, what dost thou to mine eyes,

The poem opens with the speaker talking to somebody. Who is he talking to? "Love," whom he calls a "blind fool." What’s this all about?
From Renaissance illustrations (but these ideas continue into modern popular culture), we know that this "blind fool" probably refers to Cupid, who is usually pictured as wearing a blindfold (yes, it isn’t technically the same as being blind, but you get the idea). To see a picture of blindfolded Cupid, check out this image by the Italian painter Sandro Botticelli.
Now, already we should be on the alert about something. Technically speaking, Cupid isn’t the god of Love—he’s actually the god of sexual desire. (The word "Cupid" comes from the Latin word for "desire.")
Any sort of appeal to a higher power, something that is abstract or unlikely (or unable) to reply, is what's called an apostrophe in poetry (and you thought those were just for punctuation).
Why is the speaker calling the god of sexual desire the god of Love? We’ll have to keep reading the poem to find out.
Another mystery: the speaker says that Love has done something to his eyes. What has Love done? We don’t know—but neither does the speaker (he is asking a question, after all). Let’s keep reading to find out what the deal is.

That they behold and see not what they see?

Now we get the end of the speaker’s question from Line 1. The speaker wants to know what in tarnation Love has done to his eyes to make them "behold" but "see not what they see."
Don’t worry if you find this line a little tricky—it’s supposed to be. That’s because the speaker is using (a) some old fashioned language, and (b) is punning (i.e., making some word-play) on two different meanings of the word "see."
Let’s start with the old-fashioned language. The word "behold" just means to "see" or "look at" something.
Now, let’s tackle the pun. This one isn’t really that hard—once you get it, that is. The first time the speaker uses the word "see" he means it in the sense of understanding, like when you say, "Ahh, I see how that math problem is working." The second time he uses the word "see" it means, well, "see"—in the normal sense of "look at." So, you could rephrase this whole line as asking what Love does to the speaker eyes "so that they look, and don’t understand what it is they’re looking at."
Okay, so we know what you’re wondering: "What are they looking at?" Well, the speaker actually doesn’t tell us—for some strange reason, he seems to think that if he gives everything away in Line 2, we won’t read on to the end. Weird, huh?
It looks like we don’t have much choice: we’d better read on.

They know what beauty is, see where it lies,

But wait. The speaker isn’t going to tell us right away what he means. Instead, he’s going to change the subject—sort of.
Instead of telling us what his eyes are looking at right now, he tells us about what his eyes normally do.
Normally, he says, his eyes know "what beauty is." They also "see where it lies," meaning they "see where it is." The word "lies" here is being used mainly in the same meaning as in the phrase, "Tell me where the treasure lies." (Some scholars also think that he means "lies" in the sense of "lies down," so that there’s a double-meaning here that lets you imagine the speaker’s lady-love lying down, maybe in bed.)
The MAIN meaning of the line, though, is still clear: Basically, he’s saying that his eyes are generally pretty reliable when it comes to judging beauty.
Of course, eyes don't really have a brain. Giving human qualities (like knowing) to inanimate objects (like eyeballs) is what's called personification.
But wait—back in Lines 1 and 2, wasn’t the speaker telling us that Love had made his eyes all screwed up, so that they "see not what they see"? Are you thinking what we’re thinking? Yes: there has got to be a "but" coming up right about…

Yet what the best is take the worst to be.

…now.
Here, finally, we start to get a hint of what the speaker is really talking about. The problem is, this hint is phrased in a really confusing way. Let’s see if we can make things clearer.
The problem here isn’t the words the speaker is using—it’s the order he puts them in, the syntax which is frankly really weird. The good thing is that we can simply rearrange them—without adding or removing a single word—to make the meaning come across much more clearly: "Yet take the worst to be what is the best."
But, just for fun, let’s try saying the same thing in different words, just to make 100% sure we’re on the same page: "Yet they mistake the worst thing in the world for the best thing in the world."
Okay, so that's sorted out, but what about that hint about what the speaker is talking about? Well, let’s think about it. He started off by saying that Love has tricked him and has made his eyes not know what they’re looking at. Now he says that his eyes mistake worst thing in the world for the best thing in the world. Doesn’t that kind of sound like he’s talking about a significant other who turned out significantly nasty?