So, according the the Doctrine and Covenants, the telestial kingdom (the lowest one) is under the Holy Spirit:
And again, we saw the glory of the telestial, which glory is that of the lesser, even as the glory of the stars differs from that of the glory of the moon in the firmament. These are they who receive not of his fulness in the eternal world, but of the Holy Spirit through the ministration of the terrestrial (Doctrine and Covenants 76:81, 86)
The terrestrial kingdom (the middle one) is under Jesus Christ:
These are they who receive of the presence of the Son, but not of the fulness of the Father. (Doctrine and Covenants 76:77)
The telestial kingdom is under the Father (and the Son):
These shall dwell in the presence of God and his Christ forever and ever. (Doctrine and Covenants 76:62)
This is not to say the Holy Spirit/Ghost or Jesus live in those lower kingdoms. That is not what the scriptures say, but the people in those kingdoms have proven faithful to experience either the Holy Spirit or both the Holy Spirit and Jesus Christ.
I'm thinking that mortal life reflects eternity, bearing witness to us if we have eyes to see. In other words, these scriptures could be telling us something about our own states here, in this life.
If we hear and feel the Holy Ghost and are led by Him, we are a step up from outer darkness. We see much "outer darkness" in this world. We see it in murderers, child rapists, uncontrollable anger, and so forth. If we hear, feel, are led by the Holy Ghost in this life, we are in the telestial arena. I believe many good people are in this arena, including most honestly believing saints in Jesus' own church.
If we are in the darkness, many of us search for light. We are not comfortable being in the darkness of pain, anger, and evil. According to prophesies and history, there usually reaches a point in societies where the majority of the people feel comfortable in outer darkness and refuse the light, becoming violently angry with it. Unfortunately, this slide into darkness is all too visible in our society today.
But we are going to go up, not down, in this post.
If we listen to the Holy Spirit, He brings us to truth. He brings us to Jesus' own church. Imperfect as it is, it was authorized by Jesus himself. It holds the keys it needs to have to perform its functions. It has the authority to perform ordinances that are vital for exaltation, for returning to the Father. The leaders in the general leadership have the right to inspiration and revelation from God for the benefit of the church as a whole, as a body. None of us peons have that right. It was not given to us by God and it won't be, because God's house is a house of order. Even if Jesus raises up a prophet to warn us of impending destruction if we don't repent, he (the prophet) will never presume to take authority out of the hands of the authorized leaders (i.e. "The Prophet"); he (the prophet) will speak mildly, without coercion, and with no desire to gain a following; he (the prophet) will simply point us toward Christ, as a fellow human, no better than us.
So, we accept those ordinances with a humble heart, in meekness. We obey the voice of God wherever it may be found (personal revelation, which verifies all truth whether that truth comes through ecclesiastical leaders; scriptures; inspired men, women, and/or children; dreams, visions, prayer, and so forth). Eventually, if we remain faithful and hunger after all truth, thirsting after righteousness, we are brought to a point of seeing Jesus face to face, of having our faith turned into absolute knowledge. When we reach that point, we have literally advanced from the telestial kingdom to the terrestrial kingdom – in this life.
The next step, about which I know nothing because practically nothing has been written in scripture (other than that Christ brings us to the Father), is for Jesus to bring us face to face with the Father, completing the redemption from the fall and bringing us into the celestial arena, up to the celestial level – in this life.
It's incredible, really.