Section I (Lines 1-8) Summary

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

When forty winters shall besiege thy brow,
And dig deep trenches in thy beauty's field,

Shakespeare opens this sonnet up with a metaphor, although he hides it a little bit. The image here is of an army attacking a castle.
Back in the day, if you were attacking a castle, you wouldn't be able to just blow it up, or to rush through the door, because the army inside would slaughter you. So instead you would "lay siege" to the castle. You'd dig trenches around the castle and just wait for the army inside to get so tired and hungry that they would give up on their own.
So here the young man's forehead is being compared to the wall of a castle, which is under siege by the armies of time and old age. The young man may be healthy and strong now, but time can wait as long as it needs to for him to give up, even if it takes "forty winters."
Notice also that "forty winters" means forty years, but it also calls up the pain and cold of winter. As the young man gets old, time will wreck his good looks with wrinkles, which Shakespeare compares to the "trenches" that the army is digging in the fields around the castle.

Thy youth's proud livery, so gazed on now,
Will be a tatter'd weed, of small worth held:

Now the speaker tries another metaphor, comparing youth and old age with different kinds of clothing.
In line 3, he compares the young man's youth and beauty with "proud livery" – or the beautiful clothes that a young nobleman would wear. Imagine silk and velvet and bright colors, a costume that would be admired and looked at ("gazed on") by everyone. It's a little like a young movie star going to the Oscars in a really great tux. The clothes he wears emphasize how young and carefree and beautiful he is, and everyone gathers around to take pictures, compliment him and admire him.
Now if the clothes of youth are beautiful and fresh and expensive, what do the clothes of old age look like? Not much, it turns out. All the young man has to look forward to is a "tattered weed" (that's an old term for a piece of clothing) that isn't worth much.
So, the take-away point here is that being young is a lot of fun, and when you're old, things are pretty worn out and crummy.

Then being ask'd where all thy beauty lies,
Where all the treasure of thy lusty days,

Now that our speaker has put the image of a wrinkly, tattered old man firmly in the young man's head (and hopefully has him a little scared), he pushes it a step farther.
In these lines, he asks the young man to imagine what it will be like to be that old. What will he say when people ask him what happened to his good looks (line 4)?
Line 5 basically repeats the same idea as line four, but the words are a little more complicated: when the speaker refers to the "treasure of your lusty days," he's just talking about all the strength and beauty and happiness of being young. The word "lusty" in Shakespeare's day wasn't as closely associated with sex as it is now. It meant something more like strong, healthy, and vigorous, although maybe there's a slightly sexual pun here.
So the speaker is essentially saying, "You're having fun now fooling around and enjoying your youth, but what are you going to have to show for it in 40 years when you are old and wrinkly and weak?"

To say, within thine own deep-sunken eyes,
Were an all-eating shame and thriftless praise.

Think back to line 5 where the young man has been asked the question: "Where did all of your beauty go?" Now if he were to answer, "It's still right here, I'm just a little older," it probably wouldn't fly.
Don't get us wrong, we're not trying to be ageist here, but you're probably just not going to be as hot at 60 as you are at 20. That's the idea behind this sonnet at least.
The point is to make youth look so precious and old age so bad that the young man will do anything to avoid the consequences of getting old. That's why the speaker uses the image of "deep-sunken eyes" (line 7), which makes the imaginary old man's face seem almost like a skull.
If the man were to respond that some of his beauty remained in his hollow, old-looking eyes, the speaker thinks he should be ashamed. The man would be throwing away empty praise on himself like a "thriftless" person who spends more money than he saves (line 8).