This is what Hellenists do morning and evening. The hymns are from The Orphic Hymns, translated by Thomas Taylor (which can be found online for free and printed out if you wish).
This site is very helpful for further information: www.Hellenion.org, and has many useful links.
To the Gods--Morning
Wash hands and face
Light Lamp or Candle (either works just as well)
Hymn to Hestia (# 83 in Thomas' translation) [Hestia is the Goddess of the Hearth, the Home, and Family]
--- Daughter of Kronos, venerable Dame, the seat containing of unweary'd flame;
In sacred rites these ministers are Thine, Mystics much-blessed, holy and divine
In Thee the Gods have fix'd place, strong, stable, basis of the mortal race:
Eternal, much-form'd, ever-florid Queen, laughing and blessed, and of lovely mien;
Accept these rites, accord each just desire, and gentle health, and needful good inspire.
Many Hellenists now light incense. This is not mandatory, and I've never been able to do so, though I know the Gods and Goddesses are still pleased with my prayer. Incense is not mandatory.
Hymn to Eos (# 77) [Eos is the Goddess of the Dawn, also known as Aurora, which is Her Roman name.]
--- Hear me, O Goddess! whose emerging ray leads on the broad refulgence of the day;
Blushing Aurora, whose celestial light beams on the world with red'ning splendours bright:
Angel of Titan, whom with constant round, thy orient beams recall from Night profound:
Labour of ev'ry kind to lead is thine, of mortal life the minister divine.
Mankind in thee eternally delight, and none presumes to shun they beauteous sight.
Soon as thy splendours break the bands of rest, and eyes unclose with pleasing sleep oppress'd;
Men, reptiles, birds, and beasts, with gen'ral voice, and all the nations of the deep, rejoice;
For all the culture of our life is Thine. Come, blessed Pow'r! and to these rites incline:
Thy holy light increase, and unconfin'd diffuse its radiance on Thy mystic's mind.
Hymn to Helios (# 7) [Helios is the God of the Sun, and is the father of Eos "morning light" and Selene, the more modern Moon Goddess: "Father of the Night."]
--- Hear golden Titan, whose eternal eye with broad survey, illumines all the sky.
Self-born, unwearied in diffusing light, and to all eyes the mirrour of delight:
Lord of the Seasons, with thy fiery car and leaping coursers, beaming light from far:
With Thy right hand the source of morning light, and with Thy left the Father of the Night.
Agile and vig'rous, venerable Sun, fiery and bright around the heav'ns You run.
Foe to the wicked, but the good man's guide, o'er all his steps propitious You preside:
With various founding, golden lyre, 'tis mine to fill the world with harmony divine.
Father of ages, guide of prosp'rous deeds, the world's commander, borne by lucid steeds,
Immortal Jove [Zeus], all-searching, bearing light, source of existence, pure and fiery bright.
Bearer of fruit, almight Lord of Years, agil and warm, whom ev'ry pow'r reveres.
Great eye of Nature and the starry skies, doom'd with Immortal Flames to set and rise
Dispensing justice, lover of the stream, the world's great despot, and o'er all supreme.
Faithful defender, and the eye of right, of steeds the Ruler, and of life the Light:
With founding whip four fiery steeds You guide, when in the car of Day You glorious ride.
Propitious on these mystic labours shine, and bless Thy suppliants with a life divine.
Hymn(s) to special God/dess(es) of the day (see next chapter)
Additional hymns as desired.
Pour libation. This can be as simple as some water on the ground, or as impressive as wine in a ceremony. Do what you can, the Gods and Goddesses will not be unhappy with you if you cannot do something extraordinary.
After libation, pray for yourself and your family and friends. Ask for what you need, give thanks to the Gods and Goddesses, ask for guidance, whatever it is that you feel the need to do. Ask for strength in your faith, or a sign that They are there. Believe that it will come to pass; listen for Their voices...
Orpheus to Mousaios (see next chapter)
Extinguish Lamp or Candle.