John Donne's poem, "Song" or "Goe, and Catche a Falling Starre" (to distinguish it from other poems of the same name) addresses things that are supernatural/superstitious and impossible. ("Supernatural" refers to things not of the natural world—"above" or "beyond" nature. This can refer to God, ghosts, spirits, fairies, or any creature that is beyond what is seen in the natural world.)
...the speaker is a young man. He throws out fanciful notions of impossible attainments...
The first line encourages the reader to catch a falling star, an impossible task. Catching a star is impossible, another in the speaker's list of the "unattainable."
The next item is something steeped in witchcraft. The mandrake root was supposed to grow only under the gallows where criminals were executed, and were said to be shaped like a man, scream when "harvested," and able to kill any human hand that touched it. It was also rumored to help women conceive a child. (This is totally based on folklore, and impossible as well.)
The young man then asks where the years "go?" (No one can answer this.) He also wonders who put the cleft or split in the "Divels" (Devil's) foot. The speaker then asks...
Teach me to heare Mermaides singing...
Mermaids are like the sirens in The Odyssey, when Odysseus is tied by his crew members to the mast of the ship, and the others put wax in their ears: sirens are impossible to resist when they sing, and any man that follows the siren is enthralled until she eats him. Mermaids are also said to...
...sing...and enchant [people and gods], distracting them from their work and causing them to...run their ships aground.
The next line...
Or to keep off envies stinging...
...seems simply to mean that this man would hope not to be stung by enviousness (which is foreshadowing with regard to the real focus of he poem).
Next the speaker asks to find that which can drive him (like the wind) to pursue an "honest minde."
In the second stanza of the poem, the speaker's request is much greater. He notes that if one has the ability to see "strange sights, / Things invisible...", would he ride for a thousand days and nights till he is old and white-haired, and return to tell his tales of those days, and swear that a true and beautiful woman is impossible to find:
If thou beest borne to strange sights,
Things invisible to see,
Ride ten thousand daies and nights,
Till age snow white haires on thee,
Thou, when thou retorn'st, wilt tell me
All strange wonders that befell thee,
Loves a woman true, and faire.
In essence, this is just another thing of the speaker's list of impossible things to attain/do, but the last stanza depicts the true nature of the poem. The speaker has listed many impossible things: the last of which is finding an honest, lovely woman. Here, now, he tells the listener that IF he finds such a woman, to let the speaker know. It would be a "Pilgrimage...sweet" to find her, but says he would not go, even if she lived next door, because to him, she would inevitably be false.
If thou findst one, let mee know,
Such a Pilgrimage were sweet;
Yet doe not, I would not goe,
Though at next doore wee might meet,
Though shee were true, when you met her,
And last, till you write your letter,
False, ere I come, to two, or three.
While there may be a "a woman true, and faire" somewhere in the world, the speaker must have been hurt—she is not for him. He has no faith in women.