The gods are one of the Three Kindreds, loose classifications of beings that we honour in our druidry. In ADF, our organization focuses on the gods of different Indo-European cultures, but individuals may have relationships with whatever gods or spirits speak to them. Within Indo-European cultures, there are many similarities between deities found in each one (sky gods, for example), but their cultural reflections hold many mysteries also.
It is often recommended that one honours gods of only one pantheon in each rite. This is a good general rule, especially when you are getting to know them. However, I have also participated in rites in which many warrior gods were honoured, or many bardic deities, and those rites were also beautiful and well done. You may have patrons from many hearths, and wish to honour them all at once. Your hearth religion, after all, is that religion which takes place at your own hearth. 🙂
Primarily, though not always, offerings to gods are made through the Fire, as the Fire travels upwards to the Sky. But, there are many gods who are found in many places, and they have personal preferences just as we do, so it would be well to learn these things over time. When beginning a relationship, a good drink and a good fire will generally not do you wrong.
Our Grove has six deities that we honour as Gods of the Grove — deities who we have deeper relationships with that we have developed through worship and practice, and in turn those deities have taken an interest in us. First is the Earth Mother, who we honour at every rite. Brighid is our hearth goddess, and we give offering to her when we light the hearthfire. We call upon Manannán as Gatekeeper, to aid us in better communicating with all the realms in ritual. Lugh, An Dagda, and An Cailleach are honoured at their respective holidays, and we have learned much from their wisdom.
At our personal hearth, our pantheon looks very similar. The Earth Mother and Gatekeeper are patrons of the ADF Clergy, so have a special place on our shrine. Likewise, Lugh and Brighid are our personal patrons, and they are well honoured at their own shrines. Of course, I have relationships with other deities as well: the Dawn and the Pole Star, to simply name two.
Some pagans see their primary relationships as being with the Ancestors, or with the Land Spirits, and the Gods are not as important in their practice. There is nothing wrong with that at all. For me personally, my relationships with the Shining Ones are at the core of my practice, though I do honour all the Kindreds each day.