From the get-go, we can see that our speaker is pretty close with nature. He has paid close attention to the spring and knows that, before trees and plants get to their summer-green color, they are often gold or yellow. This dude clearly knows his green and gold stuff.
Her hardest hue to hold. (2)
Our speaker is so close with nature that he personifies it as… her. She isn't able to hold on to that first gold color for long, which fits with the poem's title, "Nothing Gold Can Stay." By this point, we're pretty sure the poem is talking about the colors of spring, not precious metals.
Her early leaf's a flower; But only so an hour. (3-4)
These lines use metaphor to talk about nature, comparing a leaf to a flower. This, again, is referring to spring blooms, but it's also saying that flowers are not too different from leaves. We're starting to see what the whole "Nothing Gold Can Stay" thing is about—the quick change from spring to summer, from flower to leaf.
Then leaf subsides to leaf. (5)
It turns out our speaker prefers the early leaves to the later ones; otherwise, he probably wouldn't have used the term "subsides."
So Eden sank to grief, (6)
Perhaps the most fantasized-about natural world in existence is the biblical Garden of Eden. There, things were perfect, beautiful, and serene. There was always enough to eat, and the first humans, Adam and Eve, had no worries. But, just like blooms turn into leaves and gold turns to green, when Eve sinned by eating from a forbidden tree, Eden came to grief. Bummer, dude.
So dawn goes down to day. (7)
We've jumped from the fantastic Garden of Eden to an everyday occurrence: the change from dawn to day. Again, we see how the beauty of dawn and its brilliant colors are only temporary and give way all too soon to daylight.