When it comes to discussing the Greek gods, “chthonic” or “chthonian” is a very useful and somewhat confusing word. You’ve probably heard it applied to underworld gods and spirits, the gods some people prefer not to deal with, the gods they find scary, the gods they fear may be dangerous.
(We will leave for the moment the fact that all gods are, potentially, scary and dangerous. :))
“Chthonian” is sometimes contrasted with “Olympian” and while that is not inaccurate, it is also not the whole story. Even scholars, for the most part, no longer believe in a strict Olympian/chthonian division of deities and/or rituals. All that “chthonian” means is “within the earth.” It applies not only to underworld deities who reside within the earth such as Hades and Persephone but to agricultural deities like Demeter and Gaia. It applies to psychopomps like Hermes and Hekate, gods who visit the underworld as part of their duties but don’t necessarily live there.
Additionally, not all gods who are chthonian are chthonian at all times; a number of deities have a chthonian face (or faces) and an Olympian face (or faces). Zeus, for example: as Olympian Zeus he is the epitome of the Olympic god, but as Zeus Meilichios he is approached as a chthonian deity. Another example is Hermes: Hermes the god of the marketplace, the merchant, the gambler, in all these roles he may be approached as an Olympian god. As a psychopomp he is approached as a chthonian deity.
And when I say “approached as a chthonian deity,” I refer to some basic differences in how one may approach the god in this context. These differences are probably best taken as good guidelines rather than hard-and-fast universal rules–there was a fair amount of variation regionally and over time with regard to how one dealt with a chthonian or Olympian deity–but they are a place to start.
In some ways the offerings made to chthonian deities were more similar to those made to the recipients of hero cult, or even to those made to the dead, than they were to offerings made to Olympian gods. (I mention this both because it points again to the underworld nature of these gods, and because I plan a future post on heroes and the dead.)
* Offerings to chthonian gods were often made at night rather than in the daytime as was more usual for offerings to Olympian gods.
* Chthonian gods did not typically receive offerings of wine, preferring milder libations of milk or water mixed with honey. (The dead received wineless offerings as well, since wine was considered too heady a drink for them.) Others who preferred non-alcoholic libations were the nymphs, so this was not solely a preference of chthonic entities.
When an animal was sacrificed to a chthonian deity, it was typically preferred that it be dark in color rather than light (as was often the case with regard to sacrifices to Olympian gods).
* Worshippers did not typically share in meat offerings made to chthonic gods, which were often burnt in their entirety. (This, too, contrasts with typical offerings to Olympian gods, which ended with a feast shared between the gods and the mortals in attendance.) In cases where the meat was eaten, it was often required to be eaten immediately and could not be removed from the site (as was usual in the case of offerings made to the similarly-chthonic heroes).
* Offerings were typically made to chthonic gods, and libations were poured out, on and onto the earth itself rather than on and onto an altar.
These differences may or may not be pertinent to your personal practice; personally I almost always pour out my libations onto the ground, but that is in part because I lack an outdoor altar that would allow that. The notion of relating the specifics of worship to the nature of the gods as you are approaching them at that time, however, is I think always useful.