Polytheism, or the belief in multiple deities, is a term that is often used to describe the religious paradigm of the ancient Celts, these views being consistent with the spiritual practices of ancient cultures in general. Many Gods and Goddesses were alive and active in that world of long ago. In fact, there are several hundred names of various Gods and Goddesses currently known from Celtic languages. Of these many names, the vast majority occur only once or several times in one vicinity.
We see by looking at all of these various names that most of the deities were localized and that the cult practices specific to them were also limited to their area of influence and presence. It is as though many of them had a home territory as defined and particular as the territories of tribes. These local deities were often worshiped in a small area and were associated with a specific natural feature or a particular tribal group. Some of these local deities who were so attached to specific places may represent Gods and Goddesses who were indigenous to pre-Celtic people who later became Celtic through cultural evolution and contact with migrating or nearby Celtic peoples. Often these indigenous local Gods or Goddesses were agricultural and fertility focused and provided prosperity in that geographic area. There was no type of 'Celtic Pantheon' of deities who were universal to all Celtic peoples.
Along with this multitude of localized Deities there are, however, a few Deities whose worship- or at least whom an awareness of- can be seen distributed over a broader area and among many tribal groups. Ogma was a widely known God in Ireland who was the champion and strong man of the Tuatha de Danann. Ogmios is a name linguistically connected to Ogma and was known in Gaul and described as the Gaulish Herakles. Perhaps as the culture expanded and spread to new areas, knowledge of certain cultural Gods and Goddesses spread with them. These Deities of the people may have literally traveled with the tribes and peoples as they moved into new areas. Often these deities of the people are related to functions, crafts or arts, some of these functions, crafts or arts were being introduced to new areas by more advanced peoples and one would expect these deities to traveling with them and be embraced by people who are being introduced to these new skills or types of knowledge. It is actually quite common in cultural migrations that a new people coming into an area brought with them the Gods of their people but also recognized indigenous local Gods and Goddesses.
 Lyon and London are both places originally named after a God obviously known in both Gaul and Britain. His name preserved as Lleu in Welsh Mythic material while the God Lugh was so well known in Ireland that the name of his ancient festival is still the name of a month {[Lughnasa} in modern Irish.
These Gods and Goddesses were most likely thought of in very individual terms. We see that they had stories in the mythic material that survives. These Gods and Goddesses had their likes and dislikes, their abilities and their failings. The relationships with these Deities were based on the same type of ethical and societal contracts as those that established the relationships between the human members of the cultural group and were understood in a highly personalized manner.
Contracts of mutual hospitality were maintained between the people and the Gods or even between individuals and specific Deities. The human participants of these contracts offering piety in the form of the performance of appropriate rites and festivals including offerings and sacrifices done at the prescribed time and in the traditional manner. In return for the proper observation of the appropriate forms of piety, the people received blessings of prosperity in the certain areas of special expertise and jurisdiction of a given God or Goddess.
At times these Deities are depicted in anthropomorphic {or human-appearing} terminology or art. Descriptions of the Irish God, Midhir, go into great detail describing his appearance as a tall, beautifully dressed man with a lion-headed torc around his neck and a purple cloak about him. We know where the gate to his home is, in the Sidhe mound of Brí Leith. He was a master of game-playing and contracts, who could turn simple sounding agreements to his extreme advantage. Yet his pride led to a horrible and long lasting war among the Gods when his brother, Bodbh Derg, was elected King of the Gods instead of Midhir.
But we also see them depicted and described in zoomorphic terms in which they are animals or take the form of animals. The Irish Goddess, Boand, is a white cow and the Goddess of the river of the same name: she was even the primary Goddess of an ancient tribe who called themselves Boandraige- the people of Boand. The Irish War Goddess, Badb, is a crow. And the famous Rhiannon of Welsh background began as a horse Goddess.
We often see Deities in the mythic materials changing shape from human to animal forms. Midhir changes himself and his wife into cranes. And the Great Queen of Irish traditions, the Mor Righain is alternately seen as an old hag, a beautiful seductress, a water serpent and a crow.  In fact, she has in excess of thirty names and attributes known. Surviving Celtic mythic material is rife with shape changing. Messengers often come from the otherworld in the shape of birds, many times leaving offspring in this realm.
Human and animal attributes could sometimes be depicted as simultaneously existing in a Deity who is not shifting between the forms but has parts of each form present at once. One of the few Gods physically depicted prior to the Roman conquests of Gaul and Britain has the body of a man and is antlered like a stag. He is seen in many depictions from Northern Italy across Gaul and even in Britain, usually he is seated and has torcs hanging from his antlers or in his hands. Sometimes the animals of the forest are seen crowded around him. He is usually accompanied by ram-headed snakes which he sometimes holds and feeds and which are even occasionally depicted as appendages. Of the many representations of this wild God which we see spanning the space of numerous centuries and scattered across a wide range of Celtic speaking tribes, only one bears a name; Cernunnos.
 Emerging from all of this source material is a picture of ancient Celtic polytheism: a living image of a vibrant and active religion. We see that there were some Gods and Goddesses who were widely known and honoured over a vast range and by peoples of many differing tribes and political groups. Yet there were other Gods and Goddesses who were attached to specific locations or peoples and honoured only within a small geographic area or by a single tribal unit. Some peoples or at least their rulers claimed direct descent from some of these Deities. Taking forms such as rivers, animals, humans- or even combinations of forms- these Gods and Goddesses populate the myths and iconography of Celtic speaking peoples.
In this picture we also see that the relationships between the people and these Deities were very real and often very personal. There were social contracts in place between tribes and their Gods and Goddesses with each party-divine or human- responsible for fulfilling their obligations to the other party. We see these contracts also established between individuals and their Deities and based on the customs of Celtic hospitality. Tribes and individuals met their obligations through appropriate sacrifice and offering and by honoring the Gods and their people according to tradition and custom. But the most important thing to understand is that these Gods and Goddesses were real. They were individuals with their own feelings, thoughts and personalities. The very nature of these Gods being real and comprehensible allowed for strong interpersonal spiritual relationships between the people and the Deities that they worshiped. 
This picture inspires the modern Celt and formulates our awareness of and our relationships with our Gods and Goddesses. While the people living in modern countries that were once ancient Celtic lands can embrace and work directly with the local deities who are found in those areas, for those of us who are far geographically removed these traditional sacred locations, that is not possible. What we seem to find with Celtic spiritual groups in North America is that they worship and work with the deities that were known over a wider area and by multiple tribes. From a practical sense the deities being worshipped by these people are Gods and Goddesses of the people moreso than the Gods and Goddesses of sacred places. These Gods and Goddesses were often the deities of tribes, arts, crafts and functions and so they were the ones who moved with the people.
Quite common to have a personal patron or patroness, most modern practitionersd of Druidry have an individual relationship with one specific God or Goddess with whom they have an affinity. A writer may find that they seem to have a connection with a Goddess of poetry, an attorney may find a connection to a God of law and contracts. Healers, farmers and people who have various crafts may find that they connect with a deity who has that attribute or ability, and so the skill, craft or hobby becomes a spiritual act for them. At times, these relationships are immediate bonds that form as soon as the person is introduced to a given deity and realize that there has always been some type unnamed feeling there. It is suddenly like meeting an old friend that you had not thought about for a long time. At other times these relationships may take years to develop through a slow process of study and prayer. These spiritual relationships are usually very personal and are based on an exchange between both parties, human and divine. A person often wears a symbol of their patron/ess or has a special section of their personal altar set aside to honor that deity, perhaps with a symbol of the deity or some specific attribute. Like interpersonal human relationships, these deity-human interactions are very personal with no two relationships being exactly the same.
Often, modern groups who study and worship together will have a group patron or patroness. Like the peoples of old, these groves and spiritual tribes work together toward a common goal and will often have a group relationship with a deity that is concerned with that goal or seems to have an interest in the group as a whole. The group identity may become directly related to the identity of the patron/ess so much so that even the name that the group gives itself may reflect this relationship. Meetings or group functions may include or begin with a small ceremony or rite to offer to or honor the particular deity of the group. Ceremonies, celebrations, festivals and seasonal feasts may begin with an invitation to and honoring of the group patron/ess.