The poem begins with a strange command: "Go and catch a falling star." This is only the first of a list of impossibilities that the speaker demands of his listener.
The enchanted world the speaker begins to evoke in these first four lines is one that's both melancholy and a little sinister. To catch a falling star is plainly impossible, but the image is beautiful. Similarly, seeking "all past years" is a fool's errand, but one whose success would be deeply rewarding: think of all the lost things and lost people that one might find in those years! There's a tension in these images between longing and inevitable disappointment. The imagination can conjure how wonderful it would be to catch a star or reclaim the past, but the rational mind knows it's never going to happen.
Alongside these sad and lovely images, though, the speaker makes some rather less wistful demands. To "get with child a mandrake root"—in other words, to impregnate a creepy humanoid tuber—is less a fantasy, more a body-horror nightmare. This is a command to get involved in sexual black magic with a plant noted for its dangerous hallucinogenic properties. (See the Symbols section for more on mandrakes.) It also introduces a note of sexual menace that's going to be important later on in the poem. The juxtaposition between this image and the falling star that precedes it is jarring.
Similarly, discovering "who cleft the devil's foot" sounds like a task with less obvious rewards; if you're researching that foot, you're not only getting pretty close to a decided enemy of humankind, you're also prying into his business, and perhaps seeking knowledge that humans aren't allowed. But the image of the devil's foot as "cleft"—in other words, like a goat's hoof—lightens the image up a bit. Rather than a terrifying and powerful adversary, this goat-footed devil seems more like the cartoonish figure of folklore: a sinister trickster, certainly, but one you might be able to engage in a contest. The tone of this devil-seeking stays light and wry.
However, the introduction of the devil also inflects the images that come before it. The "falling star" might itself have a devilish quality—a fallen star is not unlike a fallen angel, as the devil was said to be. And seeking "all past years" is the sort of thing one might seek some devilish assistance with—let alone impregnating a strange root-creature.
In short: these first four lines create a vivid picture of a world full not just of impossible tasks, but impossible longings. And that world brims with sexual deviance, ugly conflict, beautiful things turning bad, and lost things that can never be recaptured.
Importantly, it does all this in the form of an apostrophe. The speaker is commanding his listener to go out and perform these tasks, and he does so in no uncertain terms, using an insistent trochaic meter (meaning that the feet follow a stressed-unstressed pattern):
Go and catch a falling star
The final trochees are cut short, thus beginning and ending the line on a stressed beat. This even, musical, but unrelenting beat helps to set the tone. This poem will be both forceful and light, imaginative and resigned, beautiful and ugly.