People ask frequently what to put on an altar or shrine for different gods. All anyone can ever give is suggestions, not guidelines, unless you’re part of a specific tradition or religion that mandates certain items. I’m compiling the general gist of what I keep telling people so that I can link this post instead of typing the same thing ^^;; I’m going to limit myself to Hellenic polytheism because there’s plenty of good posts on how to set up a shrine or altar floating around out there. Also, these are suggestions intended only as a starting point and should in no way be taken as authoritative instructions.
General gist of a shrine is a place for worship. Hellenic polytheism involves offerings; I am thus comfortable considering a space dedicated to the Theoi at which they receive offerings either a shrine or an altar or both, and I use the terms pretty interchangeably. On an altar, therefore, I would include as the basics: a symbol or icon either of the god or that reminds you of the god and a vessel of some kind for offerings. The vessel would vary based on what you plan to offer: incense needs an incense holder, libations need a dish, candles need candleholders and a fireproof environment, flowers might need a vase, etc.
I would then add anything that I want to dedicate to the god or anything that reminds me of the god and will thus aid in my worship. This might include devotional jewelry, candles, incense, crystals or precious stones, an altar cloth, statuary or figurines, trinkets, anything. I would select these items based on established symbols of the god and on personal associations I have. For instance, there’s a ballerina figurine on my shrine to Aphrodite – not because Aphrodite is the goddess of ballerinas, but because ballerinas indicate grace and beauty and strength to me, and those are very Aphrodite attributes.
Some suggestions, purely as a starting point, based on some of the symbols and myths of the major Theoi (and colors based rather more loosely on the myths and more on my personal associations). This list is in no way exhaustive and will probably be added to:
Zeus: bull, eagle, swan; thunderbolt; oak; Pegasus; throne; diadem or royal accoutrements; a Magnum condom (flattery never hurts!); rainwater; a pebble or rock wrapped in fabric (as if a swaddled baby); goat or cornucopia; a representation of a mountain (for Olympus); the aegis; representations of any of his attendants (Ganymede or Nike, for instance); wedding rings or a gavel or scales (god of oaths); gray (especially dark), blue, purple, and gold
Hera: peacock, cuckoo, cow, hawk, crane, lion; the Golden Fleece; a wheel (bonus points if it’s on fire!); pomegranate, golden apples, lotus/waterlilies, willow; wedding rings, veil, garter, bouquet, anything wedding related; divorce papers (hey, if one, than the other, right?); representations of any of her attendants (Hebe, Eilythia, Iris, or the Horae, for instance); a child’s pacifier or baby’s bottle, or anything else to do with childbirth; a crown, scepter, or other royal accoutrements; purple, emerald green, cerulean, white, and gold (and peacock colors altogether tbh)
Poseidon: bull, horse, seahorse/hippocampus, dolphins, kraken/sea monsters; salt water; trident, chariot; ships, boats, jet skis; fishing apparatus; bridle, saddle; a split or broken rock (or representation thereof); wells, islands; the Minotaur; arguably therefore the labyrinth; maaaybe Pegasus; gray, green, blue, white, silver
Demeter: snakes/winged serpents/dragons, pig, gecko, turtledove, screech owl, mouse or field rodent (personal association because grains); maaaybe a horse but personally I wouldn’t want to remind her; bread, grains, wheat ears, corn, barley; basically all fruits and vegetables; mint, poppy; cornucopia; mortar and pestle (personal association) or millstone/representation of mills; anything related to motherhood; plow, sickle, or scythe (or other planting/harvest implements), or garden tools; dirt/soil; seed packets; torch; basket; hooded cape or veil; brown, green, gold
Hestia: torch, hearth, candle, lamp; coffee mug, tea bag; teapot, tea cup; head covering, veil (as of modesty), fancy church hats; fancy gloves; bread, honey; a flowering branch; a representation of a door or gate; warm oranges, yellow, gold
Athena: owl, serpent, rooster/cock; armor, a crested helmet, spear, shield; Medusa’s head; Nike; maaaybe Pegasus; a bridle (bonus points if gold); a plow; a rake; a compass; a ship; olive (tree, oil, leaf, etc); loom, shuttle, spindle, needle and thread; arguably, anything signifies scientific or mathematic advancement, such as calculators, flasks, digital scales, a lighter; pipes; literally anything that represents intelligence or making things; gavel or scales or justice’s blindfold; light blue, dark blue, gray, gray-green, light brown
Artemis: (hunting) dogs, bears, boars, deer, buzzard-hawk, some kind of sea-bird (osprey? kingfisher?), quail/partridge; game fish, rabbits; cypress, walnut, amaranth; hunting supplies, including guns, bows, arrows, fishing rod, snares, nets, etc; hunting gear, including camo; anything representing childbirth, including prenatal vitamins or baby blankets; animal skins or animal skin patterned things; Orion; anything representing young girls (prepubescent) specifically, but good luck making that not creepy; moon shaped things; lyre; torches; browns, black, red, green, white, silver
Apollon: (crow or?) raven, laurel, hyacinth; lyre, musical instruments; laurel wreath; bow, arrows, quiver; darts; discus; bandaids, bandages, any healing ointments, aspirin, anything else related to fixing broken/sick people; a therapist’s business card; sun-shaped anythings; golden flowers; snakes/dragons for the Python he killed? might be seen as rude; any tools for divination or things evocative of divination, prophecy, or oracles; herd animals such as cattle or sheep; books; philosophy; poetry; diplomas or degrees; basically anything Greek- or Classical-styled, including columns or pottery; any of his attendants or children (the Muses, Orpheus, or Asklepios, for instance); orange, yellow, white, gold, green
Hermes: tortoise, ram, hawk, hare (more Roman, but eh); crocus, Greek strawberry-tree, reasonably also “real” strawberries; winged sandals, winged cap, caduceus; stamps, postcards, shipping labels; debate team medals; divination tools, especially dice, pebbles, or lots; herd animals such as cattle, sheep, goats, horses, mules; animal husbandry tools in general; pipes or musical/rustic instruments; bucolic poetry, photographs of the countryside or rural landscapes, fables and folktales; money, tokens, coupons, tickets, anything made for exchanging value; roads, maps, model cars, representations of travel; herms, carved phalluses (idk plurals); representations of Pan, satyrs, or nymphs; workout clothes, shoes, running gear, wrestling gear; newspapers, journals, print media; your cellphone (if you want it to work forever but in a really weird way probably); arguably a peacock or feather; report card, grade sheet, assignment sheet; credit card, checkbook; literally anything with wings; whatever stands for “sarcasm, lies, and trickery” to you; therefore probably an okCupid account; stars and planets (astronomy); horoscopes and zodiac stuff (astrology); trumpet or anything that says “herald” to you; white, gold, brass, copper, brown, sky blue
Ares: dragons/big snakes, woodpecker, vulture, barn owl, eagle owl; armor, war paraphenalia, medals or honors; police badge or sheriff’s star; weapons in general including blades or guns; (fire-breathing) horses and/or his chariot; representations of any of his attendants; anything that represents fear; serpent fangs or shark’s teeth (personal leap); purple, red, bronze, gold
Aphrodite: dove, sparrow, goose, hare, cupids; myrtle, (golden) apple, red rose, anemone, narcissus/daffodil, myrrh, lettuce, pomegranate; hearts, lingerie, anything sexytimes; perfume; mirror, feathers; silk or lace anythings; love letters; makeup; a diary; bubbles; seashells; shell jewelry; also any other jewelry; a girdle or hella fancy belt; ballet slippers; fancy dress; representations of any of her children or attendants (Eros, the Kharites, or Priapus, for instance); red, pink, sea-blue, white, gold
Hephaistos: donkey/ass, crane, robots; smith or jeweler’s tools; hammer, tongs; metals of any kind, especially worked; nuts, bolts, screws; fire; representations of volcanoes; stones, especially raw; wood boards, chips, disks, etc; net (especially metal); Pandora; forged armor, forged weapons; necklace (for Harmonia’s); red, brown, brass, bronze, copper, silver, gold
Dionysos: goat, donkey, serpent, bull; lions, leopards, lynxes, tigers; dolphins; thyrsos; ivy crowns; vines, grapes, wine; apples, figs, berries, silver fir, cinnamon, bindweed; honey; seriously tho all the wine; masks, party supplies, confetti, glitter, streamers; hallucinogens/entheogens; drug paraphenalia; high heels; wilderness, especially forest or jungle; comedy and tragedy masks; stage accoutrements; feather boas; the labyrinth (through Ariadne), a crown (Corona constellation); (if Orphic bunches of other things); chalice, goblet; Mardi Gras beads (suck it up); purple, green, black, silver, gold
Haides: (three-headed) dog, black horse(s), black cattle, screech owl; cypress, mint, white poplar, asphodel; seeds, acorns; (rough) jewels or crystals; metals; coins (as in, those left on the eyes of the dead); pomegranates; cornucopia; bird-tipped sceptre; golden chariot; helmet; (golden) throne; (golden) keys; anything representing wealth; anything representing death or the other chthonic deities; bones; hotel keys; grave dirt or other cemetery souvenirs; black, somber colors, silver, gold
Persephone: narcissus/daffodil, asphodel, pomegranate, mint; sheaf(s) of grain; a torch; a throne; a crown; flowers, fresh or pressed/dried, especially roses, crocuses, violets, irises, hyacinths, narcissus/daffodils; seeds; keys; curse tablets or cursing materials; anything that represents the dead/death; fresh water (to represent the spring of Memory); ghosts; representations of the other chthonic deities, such as the Erinyes; tools of necromancy; black and somber colors as Queen of the Underworld, light colors as Kore goddess of spring