Offerings are gifts to the gods, ancestors and spirits. They are meant to please them, appease them, and sustain them. Offerings are generally symbolic in nature and therefore are not always monetarily valuable. Offerings are usually something that the deity/ancestor/spirit is known to like from their mythology, lore or history, or something from the deity's domain. Many deities also have traditional offerings that ancient cultures once offered up to them. The point is that you are making the sacred act of sharing what you have with the powers. Common offerings are beer, wine, cider, mead, honey, milk, butter, salt, bread, grains, corn meal, meat, fruit, herbs, tobacco, incense, candles, silver, jewelry, songs, poetry, art and crafts. Many neo-pagans do not offer meat because of their belief that animal and blood sacrifices are unethical and archaic. Offerings are usually returned to the earth, either by burying them or leaving them at the bottom of a tree or on a stone but they may be offered into a fire or dropped into a body of water.
Sacrifices are personal offerings of something that is valuable to the supplicant. They are almost always made in a ritual context but may also be made informally whenever there is an appropriate fire burning, body of water available, or hole in the ground for you to offer into. Sacrifices can be given to an appropriate recipient/representative of the deity's domain, but usually a sacrifice is permanently taken out of circulation once it has been made. Commonly they are destroyed and ritually disposed of in some other way. A sacrifice may be the first or last of something, something you have created or laboured over, something that is meaningful or sentimental to you, something you have spent your savings on, something you are proud of or something that is useful to you, something you need. The point is that you are ritually giving something up. Common sacrifices are money, silver, jewelry, food, drink, livestock, harvested fruits and vegetables, tools, handicrafts, artworks. Sworn oaths can also count as sacrifices if they are regarding actions one will take, such as community service work; or abstain from, such as an habitual indulgence. Again, most neo-pagans do not sacrifice livestock because of the modern belief that animal and blood sacrifices are inappropriate. In Wiccan liturgy, the Charge of the Goddess states that she does not require anything in sacrifice. Not all deities want you to put yourself out for them. In place of a sacrifice, some deities require obligations; certain sacred duties or actions that you add to your life, rather than giving up.
Libations are drink offerings, made formally in ritual or informally at any time when one is drinking. Often food is offered with them. Libations can be made to the gods, spirits, ancestors or outdwellers. They are meant to sustain the kindred and appease the outdwellers. Libations can be poured into an offering bowl on the altar or directly onto the ground if you are outside. In some traditions, libations are poured with an oath, boast or praise offering. To the Hellenes, Hestia received the first libation. The point is that you are thinking fondly of the Powers as you drink. Libations can be anything you are drinking or that the kindred would drink. Common libations are water, blessed water, wine, blessed wine, beer, whiskey, mead, other alcohol, cider, juice, but I wouldn't reccommend offering up a slushie to just anyone. I have never heard of people pouring other valuable liquids as libations, such as gasoline, but it's something to consider if you wish for the gods to assist you in some specific way.
In ADF tradition, it is common to ask for feedback on your offerings and sacrifices. After the offerings and main sacrifice have been made, the seer divines whether or not the gods accept the offerings and what blessings they offer in return. It is part of the ghosti relationship, hospitality. The principle of a gift for a gift. As a druid, I give so that all may freely give.
Offerings, sacrifices and libations can frequently be part of a transaction with a deity or spirit. We want something from them, and so we offer or sacrifice to them in order to establish or maintain a relationship of reciprocation. Many offerings and sacrifices can be made simply to maintain this relationship, without a specific need or desire on the part of the supplicant. Sometimes we ask for blessings in return, in general.
However, other times we simply make the offerings and sacrifices because we feel love, awe, or gratitude. We may make them just because it feels right or good to do so, asking nothing in return.
It is important to offer or sacrifice only what you can. If you can't reasonably give something up, or can't afford to give up as much as you'd like to, don't be a martyr. The kindred will not be impressed, and they may teach you a lesson in moderation at best. Similarly, it should go without saying to never offer something that is not yours to give. I once saw a woman bum a pinch of tobacco from another woman to offer into the fire, and I wondered how well that offering would be received.
You can find out what a god or spirit usually wants by reading mythology and lore about them. You can find out what a deity or spirit wants from you by meditating on their domain, associations and context, communicating with them as part of a personal relationship, or invoking them and discovering what they partake in and take interest in. You may have to get creative with your offerings; if you can't find something from the ancient world, you may have to find it's modern equivalent. If your deity is from another culture, you may have to offer a local equivalent of their desire. If you know the type of thing they like, a quality or attribute but not an example, you might have to use your imagination.