The Christian/Jewish/Islamic (C/J/I) model (excluding some esotericists somewhere) is petition. They petition their GOD with prayer and if they move HIM then their petition is answered. No actual power exists in the supplicant and all power (except for satans, devils etc.) exists in GOD.
The nature of the pagan gods, spirits of the land and the ancestors seems different. No one god or goddess is all powerful. Even in the Greco-Roman pantheons, the thunder god had to look out if his wife was angry:-) But, the ancient model was still of propitiation and supplication. Giving offerings and honor and prayer and reminding deities and spirits of longstanding national/ethnic/family relationships served much the same purpose as prayer and supplication to the C/J/I GOD - at least in part.
The part that may be different is based on the nature of our relationship to deity. Our gods, the ancestors and the spirits of the land need us. They have desires that may be longstanding or they may be immediate and they cannot be consummated in this world without our help. In my own belief, They are here, in this world only through us and other sentient beings.
When we reach out in meditation and ritual we invite Their attention. We acknowledge Them and, over time, They may acknowledge us. From this contact bonds of love, honor and respect may grow. While They glow brightly and we glow less so, still, there is an equality. We receive gifts from Them based on their natures - sometimes things asked for and sometimes things just given. And They receive gifts from us according to our natures - perhaps even doing their work in this world as we understand it.
The key, in my mind, is according to our and Their natures. Our nature may be highly reverential or it may be combative. It may be highly intellectual or simply knowing and accepting. Their nature may be kind or demanding or kind and demanding or cruel and giving. We find each other, Gods and their people, in this reaching out and exchange of gifts. We love Them for who they are and They love us and need us for who we are.
So what happens in a healing ritual or when we work with Spirit to provide support? I believe that They enter this world with us and for a brief while, we may be infused with some insight, skill or strength of the Otherworld. It is not our skill that causes it to happen, but it is mutual love, honor and respect. From this position, if our intent is clear and in tune with Their natures, we have some short-lived abilities to do both Their and our work in this world. Short-lived because the extra insight, strength or skill is based on a relationship which we can not stay in full time and stay sane. Our and Their work because the relationship is based on our combined natures. Together, we produce a third thing of wonder - not fully us or fully Them but both us and Them.
I had struggled with the ogam letters written on twigs. There was no problem with divination - that is asking not doing. And in retrospect, there was no issue when fully in tune with relationship, that third thing where clarity, purpose and the means to fulfill that purpose are all fully present. The problem came with trying to do good while not being in relationship and not being clear. I can see now that was the issue - that the deep work of healing and support requires connection and joint purpose as a prerequisite and to work without being in that state of grace will not succeed (at least for me).