How did Hades get to know Persephone?
Most Greek accounts - even the otherwise extraordinarily comprehensive mention in the Hymn to Demeter - don't mention the cause of Hades' infatuation with Persephone. I would tempted to snarkily write it off as another flight of fancy (albeit a high-profile one) by an Olympian, which happens quite often. But what's interesting is that at least on Latin - not Greek - account does mention motivation, specifically, that Erycina (Aphrodite) had Cupido (Eros) make Hades fall in love so they could "conquer" the underwold with love.
This account is by Ovid:
Tyrannus [Haides] had left his dark domains to and fro, drawn in his chariot and sable steeds, inspected the foundations of the isle. His survey done, and no point found to fail, he put his fears aside; when, as he roamed, Erycina [Aphrodite], from her mountain throne, saw him and clasped her swift-winged son, and said : `Cupido [Eros], my child, my warrior, my power, take those sure shafts with which you conquer all, and shoot your speedy arrows to the heart of the great god to whom the last lot fell when the three realms were drawn. Your majesty subdues the gods of heaven [and sea] . . . Why should Tartara (Hell) lag behind? Why not there too extend your mother’s empire and your own? The third part of the world’s at stake, while we in heaven (so long-suffering!) are despised--my power grows less, and less the power of Amor [Eros]. Do you not see how Pallas [Athene] and Diana [Artemis], queen of the chase, have both deserted me? And Ceres’ daughter [Persephone], if we suffer it, will stay a virgin too--her hope’s the same. So for the sake of our joint sovereignty, if that can touch your pride, unite in love that goddess and her uncle [Haides].’ So she spoke. Then Cupido, guided by his mother, opened his quiver and of all his thousand arrows selected one, the sharpest and the surest, the arrow most obedient to the bow, and bent the pliant horn against his knee and shot the barbed shaft deep in Dis’ [Haides’] heart.
Ovid, Metamorphoses 5. 462 ff (trans. Melville)
This is an interesting twist, because it implies that Hades (referred to as "Dis") was not at fault here. The personification of love in Greek and Roman mythology is complicated, and sometimes love occurs without divine intervention. This is implied to be the case in most Greek writings of the abduction of Persephone, and so details are not given. The account from Ovid's Metamorphoses is distinctly different.
In most other accounts, though, Greek and Roman? Hades/Dis happens to be out of the Underworld, sees her and falls in love on cue.