Persephone – The Poems of Sappho
I saw a tender maiden plucking flowers
Once, long ago, in the bright morning hours;
And then from heaven I saw a sudden cloud
Fall swift and dark, and heard her cry aloud.
Again I looked, but from my open door
My anxious eyes espied the maid no more;
The cloud had vanished, bearing her away
To underlands beyond the smiling day. 
Persephone [pər-ˈse-fə-nē] is the Greek Goddess of spring growth and the Goddess Queen of the underworld, married to Pluto (Hades). She is the daughter of Zeus and Demeter, and her myth explains the causes of Spring and Autumn. She was worshiped alongside her mother Demeter in the
Eleusinian Mysteries. She has many names, but the most common are Kore and Persephone. She is referred to as Kore when she is Earth-side, bringing Spring to the land by her return as Demeter rejoices. As Persephone, she is the Queen of the Underworld for the dark half of the year, aiding Hades in the receiving of the dead.
“The cult of Persephone was especially strong in Sicily and southern Italy, and besides the Eleusinian Mysteries at Eleusis there were sanctuaries to the goddess across the Greek world, most notably at Locri Epizephyrii, Mantinea, Megalopolis, and Sparta. Here annual festivities celebrated Persephone’s marriage and her picking of flowers. The Thesmophoria was a Greek-wide celebration of the goddess and her mother. Exclusive to women, it was held annually before the sowing period when sacrifices were made and putrefied pig’s remains were mixed with the seeds. Persephone, in her guise as Queen of the Underworld, was often appealed to in curse tablets and on the inscribed gold leaves buried with the dead followers of Orphism which gave instructions on how to conduct themselves in the after-life.” 
Her myth is controversial because of the many interpretations and the name of one of the myths. The Rape of Persephone has been interpreted metaphorically as well as literally, and it is up for personal interpretation as well. I believe that Persephone was at first taken against her will, given to Hades by Zeus to be his wife, but later, when offered the pomegranate seeds, she ate them of her own free will. She did this knowing that once you eat the fruit of the Underworld, you cannot leave.
You can read pieces of the myth below from Homer, and I will link to other sites as well so you can make your own interpretation. There are many ways you can honor Persephone in your life and practice. One of the main things to do to honor Persephone is to leave offerings of fresh flowers on your Altar. According to Theoi.com, asphodel is a sacred flower to Her . If you have this available to you, this would be the recommended offering. Another offering would be anything related to pomegranates. You can also learn her hymns and recite them. One is listed for you below.
 XXVIII. TO PROSERPINE [PHERSEPHONE]
Daughter of Jove [Zeus], almighty and divine, come, blessed queen, and to these rites incline:
Only-begotten, Pluto’s [Plouton’s] honor’d wife, O venerable Goddess, source of life:
‘Tis thine in earth’s profundities to dwell, fast by the wide and dismal gates of hell:
Jove’s [Zeus’] holy offspring, of a beauteous mien, fatal [Praxidike], with lovely locks, infernal queen:
Source of the furies [Eumenides], whose blest frame proceeds from Jove’s [Zeus’] ineffable and secret seeds:
Mother of Bacchus [Eubouleos], Sonorous, divine, and many-form’d, the parent of the vine:
The dancing Hours [Horai] attend thee, essence bright, all-ruling virgin, bearing heav’nly light:
Illustrious, horned, of a bounteous mind, alone desir’d by those of mortal kind.
O, vernal queen, whom grassy plains delight, sweet to the smell, and pleasing to the sight:
Whose holy form in budding fruits we view, Earth’s vig’rous offspring of a various hue:
Espous’d in Autumn: life and death alone to wretched mortals from thy power is known:
For thine the task according to thy will, life to produce, and all that lives to kill.
Hear, blessed Goddess, send a rich increase of various fruits from earth, with lovely Peace;
Send Health with gentle hand, and crown my life with blest abundance, free from noisy strife;
Last in extreme old age the prey of Death, dismiss we willing to the realms beneath,
To thy fair palace, and the blissful plains where happy spirits dwell, and Pluto [Plouton] reigns. 
Orpheus – Myths of the World
“Demeter, knowing that one of the Gods had carried off Persephone against her will, and knowing that what was done had been by the will of Zeus, would go no more into the assemblies of the Olympians. She quenched the torch that she had held in her hands for nine days and nine nights; she put off her robe of Goddess, and she went wandering over the earth, uncomforted for the loss of her child. No longer did she appear as a Goddess gracious to men; no longer did she bless their fields. None of the things that it pleased her once to do would Demeter do any longer.” 
Homeric Hymn – The Rape of Persephone – III The Return of Persephone
“Now when all-seeing Zeus the loud-thunderer heard this, he sent Argeiphontes [Hermes] whose wand is of gold to Erebos, so that having won over Aides with soft words, he might lead forth chaste Persephoneia to the light from the misty gloom to join the gods, and that her mother might see her with her eyes and cease from her anger. And Hermes obeyed, and leaving the house of Olympos, straightway sprang down with speed to the hidden places of the earth. And he found the lord Aides in his house seated upon a couch, and his shy mate with him, much reluctant, because she yearned for her mother. But she was afar off, brooding on her fell design becuase of the deeds of the blessed gods. And strong Argeiphontes [Hermes] drew near and said : ‘Dark-haired Aides, ruler over the departed, father Zeus bids me bring noble Persephone forth from Erebos unot the gods, that her mother may see her with her eyes and cease from her dread anger with the immortals; for now she plans an awful deed, to destroy the weakly tribes of earth-born men by keeping seed hidden beneath the earth, and so she makes an end of the honours of the undying gods. For she keeps fearful anger and does not consort with the gods, but sits aloof in her fragrant temple, dwelling in the rocky hold of Eleusis.’
So he said. And Aidoneus, ruler over the dead, smiled grimly and obeyed the behest of Zeus the king. For he straightway urged wise Persephone, saying : ‘Go now, Persephoneia, to your dark-robed mother, go, and feel kindly in your heart towards me : be not so exceedingly cast down; for I shall be no unfitting husband for you among the deathless dods, that am own brother to father Zeus. And while you are here, you shall rule all that lives and moves and shall have the greatest rights among the deathless gods : those who defraud you and do not appease your power with offerings, reverently performing rites and paying fit gifts, shall be punished for evermore.’
When he said this, wise Persephoneia was filled with joy and hastily sprang up for gladness. But he on his part secretly gave her sweet pomegranate seed to eat, taking care for himself that she might not remain continually with grave, dark-robed Demeter. Then Aidoneus Polysemantor (Ruler of Many) openly got ready his deathless horses beneath the golden chariot. And she mounted on the chariot, and strong Argeiphontes [Hermes] took reins and whip in his dear hands and drove forth from the hall, the horses speeding readily. Swiftly they traversed their long course, and neither the sea nor river-waters nor grassy glens nor mountain-peaks checked the career of the immortal horses, but they cleft the deep air above them as they went. And Hermes brought them to the place where rich-crowned Demeter was staying and checked them before her fragrant temple.” 
I will never feel like I do Persephone justice. She is a Goddess that I feel extremely drawn to and it is hard to explain the feeling I get when I think of Her. To me, She is protection and justice as well as innocence and love. Veneration is a word that sticks in my head when I think of Her, and it fits.