The Odyssey has two passages about the Sirens. First, Circe’s warning to Odysseus (as related by Odysseus to the Phaeacians), some of which was quoted in the question:
“First you will come to the Sirens who enchant all who come near them. If any one unwarily draws in too close and hears the singing of the Sirens, his wife and children will never welcome him home again, for they sit in a green field† and warble him to death with the sweetness of their song. There is a great heap of dead men’s bones lying all around, with the flesh still rotting off them. Therefore pass these Sirens by, and stop your men’s ears with wax that none of them may hear; but if you like you can listen yourself, for you may get the men to bind you as you stand upright on a cross-piece half way up the mast,‡ and they must lash the rope’s ends to the mast itself, that you may have the pleasure of listening. If you beg and pray the men to unloose you, then they must bind you faster.”
Homer. Odyssey 12.39–54. Translated by Samuel Butler (1900). Perseus Digital Library.
† “Green field” here is Butler’s translation of λειμῶνι, which Liddell & Scott gloss as “any moist, grassy place, meadow”. ‡ The Greek here is ἱστοπέδῃ, “a piece of wood set in the keel to which the mast was bound” (Liddell & Scott) but perhaps Butler thought that half-way up the mast was a more dramatic position for Odysseus to be bound.
Second, Odysseus’s narrative of the encounter (again, as told to the Phaeacians):
Then, being much troubled in mind, I said to my men, ‘My friends, it is not right that one or two of us alone should know the prophecies that Circe has made me, I will therefore tell you about them, so that whether we live or die we may do so with our eyes open. First she said we were to keep clear of the Sirens, who sit and sing most beautifully in a field of flowers; but she said I might hear them myself so long as no one else did. Therefore, take me and bind me to the crosspiece half way up the mast;† bind me as I stand upright, with a bond so fast that I cannot possibly break away, and lash the rope’s ends to the mast itself. If I beg and pray you to set me free, then bind me more tightly still.’
I had hardly finished telling everything to the men before we reached the island of the two Sirens, for the wind had been very favorable. Then all of a sudden it fell dead calm; there was not a breath of wind nor a ripple upon the water, so the men furled the sails and stowed them; then taking to their oars they whitened the water with the foam they raised in rowing. Meanwhile I look a large wheel of wax and cut it up small with my sword. Then I kneaded the wax in my strong hands till it became soft, which it soon did between the kneading and the rays of the sun-god son of Hyperion. Then I stopped the ears of all my men, and they bound me hands and feet to the mast as I stood upright on the crosspiece; but they went on rowing themselves. When we had got within earshot of the land, and the ship was going at a good rate, the Sirens saw that we were getting in shore and began with their singing.
So the Sirens sit on a grassy or flowery meadow on an island, surrounded by the bones of their victims, and Odysseus’s companions had to steer the ship close to the shore before Odysseus could hear the singing. Therefore Homer asks us to imagine a scene something like this (but with fewer Sirens and more skeletons):
Thomas Moran (1900). Ulysses and the Sirens.
It can be difficult, however, to imagine the scene as described by Homer, because of two very different traditional depictions of Sirens in art: first, as birds with the heads of women (below left: red-figured stamnos in the British Museum, catalog 1843,1103.31), and second, as mermaids (below right: Herbert James Draper (1909), Ulysses and the Sirens).