The story of her being born from Ouranos severed member is from Hesiod's Theogony:
And so soon as he had cut off the members with flint and cast them from the land into the surging sea, they were swept away over the main a long time: and a white foam spread around them from the immortal flesh, and in it there grew a maiden. First she drew near holy Cythera, and from there, afterwards, she came to sea-girt Cyprus, and came forth an awful and lovely goddess, and grass grew up about her beneath her shapely feet. Her gods and men call Aphrodite, and the foam-born goddess
Where her lineage from Zeus and Dione is presented in Homer's Illiad. Book 5 makes repeated reference to her parentage. These segments, for instance, which refer to her father:
I am only following your own instructions; you told me not to fight any of the blessed gods; but if Jove's daughter Venus came into battle I was to wound her with my spear.
And her mother:
But Venus flung herself on to the lap of her mother Dione, who threw her arms about her and caressed her...
According to Plato's Symposium, these actually represent two different entities: Aphrodite Ourania ("heavenly") and Aphrodite Pandemos ("common"):
One, older obviously, is the daughter of Uranus and had no mother, and we call her "Heavenly Aphrodite"; the younger is the child of Zeus and Dione and we call her "Common Aphrodite". It follows then that the Love who works with the latter Aphrodite should correctly be called "Common Love" and the other "Heavenly Love"