Find something to represent the deity in question: picture from the internet, a symbol, a rock, a book, a cup, a doll, whatever. Set the image up on a table. Pour wine, vodka, good fruit juice, olive oil, milk, beer, kefir, perfume, or another fine beverage or liquid in a bowl or cup before the image. (Unless the deity in question has a history of wanting something like kool-aid or soda pop, you may want to avoid these.) If you’ve not been able to find out what liquid would be appropriate, go with your gut feeling. Bow down, prostrate yourself before the deity’s image, and pray. If you’re in this situation, the best prayer you can make is the one that is honest—there’s no formula here, no magic words, no formulaic incantation.
Do not consume the liquid that you pour for the deity. Wait a cycle of a full day and night, then pour the liquid into the earth outside. Yes. Pour it into the earth. It is not "wasteful"--it was given to a deity and the deity consumed the essence of the liquid. By pouring it out, you are completing the process of sending it on to the deity. By drinking it instead, you may have interrupted this process (again, it can depend on context).
Then she got flack from various quarters, offended at the idea that they should not consume the offerings themselves.
Galina Krasskova came to Tess's aid. After pointing out that her entry was specifically about deities one does not know -- and not those longstanding relationships where sharing the offerings might be an established practice -- she concludes:
(W)e act as though it is such a burden to give the least amount possible to our Gods. It should be a joy to give as much as we possibly can. ..and we wonder why our community is so fucked up. To my mind, it starts right here: with the penury, stinginess, and downright hostility toward sharing anything with the Gods. It starts right here. We have the community we deserve and oh we are so incredibly fucked.
Tess wrote a follow-up here, with links to some of the criticisms.
I generally don't share in the offerings I give to my gods, although we do allow our household canine nature spirit to consume offerings to Frigga after a period of time. It's not because I fear the gods would be offended or insulted so much as a desire for the gift to be a gift. However, we have ample evidence that offerings to the Greek and Roman gods often came in the form of a public event including a meal shared with the gods -- i.e., the people ate the meat, the gods got the bones and fat as a burned offering.
So I come down right in the middle on this topic. I do not agree that offerings should never be consumed by the offeror, but I do think it's a very good idea to not do so until you're sure it's ok with the deity in question.
Mostly, I would like for everybody to stop fighting over such things. Eat or don't eat the offerings as you choose, and let others find their own devotional practices. There is no pagan Pope or Magisterium to divine proper doctrine and enforce it on the laity in our religion. Discuss, debate and disagree as needed, but then go forward as fellow travelers on the path.