10. Offerings – historical and UPG.
Historical sacrifices to Hestia include cows that were a year old, as well as fruit (such as apples, figs, pears, and plums), particularly the first fruits, olive oil, sweet wine, and fresh water. It is possible that pigs were also sacrificed to Hestia. Hestia is said to have received a small first portion of any sacrifice made to any deity, often a bit of fat.
Hestia was honored at the household hearth, and this was said to be done by offering a bit of the family meal each day. Some say this was done for every meal, while other sources seem to imply that this offering would likely be part of the main meal of the day, supper. For many Greeks supper would have consisted of things like bread, vegetables, legumes, fruit, and fish. Meats like beef and pork were often special treats during festivals when a sacrifice had been made, but some were able to afford meat more frequently, or lived in an area where meat would be a bit more common.
The Orphic hymns suggest burning aromatic herbs as an incense for Hestia, which may have included things like bay leaves, lavender, chamomile, mint, coriander, and thyme. Frankincense was also likely a common incense offering.
My daily offering to Hestia tends to stick with the idea of giving a bit of dinner. The food itself is rarely traditional (the ancient Greeks probably didn't eat a lot of tacos, but I sure do), but the idea is the same, to offer a small portion of the meal (usually about a spoonful) before sitting down to eat.
For a larger celebration, I tend to stick to the more "traditional" things, like bread, fruit, cheese, olives, honey, salt, sweet cakes, fresh flowers, and so on. However, I have also found that offerings of rice, Japanese plum wine, myrrh, and sandalwood are also all appreciated - although I suppose none of those are really strange, they're all quite similar to the more traditional offerings of grains, sweet wine, and aromatics.
I have also found there's not much demand for non-perishable goods. Where I might put keys on Hekate's shrine, or waterfowl feathers on Artemis's shrine, the hearth shrine tends to remain simple and uncluttered.
Offerings don't always have to be of physical goods, of course. Mindfully keeping your kitchen tidy/home in order, or volunteering at (or donating to) a food bank are two ways one might offer their time to Hestia.