If you're not familiar with Fushigi Yuugi, you're probably a little confused by the whole miko/seishi thing, so I will explain it to the best of my ability.
Miko: This means "shrine maiden" or "priestess". In other words, the supposed link between humans and the gods. In the Fushigi world this term applies to the four girls Okuda Takiko, Ousugi Suzuno, Yuuki Miaka and Hongo Yui, who came from "the other world" and summoned the four animal gods.
The four gods:
Shichiseishi: "shichi" meaning 'seven', "seishi" meaning something like 'star warrior'. This are the guardians of the miko and give her power. Each seishi represents one of the constellations ruled by their gods. The constellations are:
Tamahomeboshi (Cancer),
Hotohoriboshi (Hydra),
Nurikoboshi (Hydra),
Chirikoboshi (Hydra),
Chichiriboshi (Gemini),
Tasukiboshi (Crater) and
Mitsukakeboshi (Corvus) - the seven southern constellations.
Tataraboshi (Aries), Koekieboshi (Aries), Tokakiboshi (Andromeda), Subaruboshi (Taurus), Amefuriboshi (Taurus), Karasukiboshi (Orion) and Torokiboshi (Orion) - the seven western constellations.
Tomiteboshi (Sagitarius), Hikitsuboshi (Aquarius), Urukiboshi (Aquarius), Urumiyaboshi (Aquarius), Hatsuiboshi (Pegasus), Nanameboshi (Pegasus) and Inameboshi (Capricorn) - the seven northern constellations.
Taitsukun: The creator-goddess and the one who keeps the universe in order. She rules over the element of void. Although she often takes the form of an ugly old woman, Taitsukun can also appear as a beautiful young man. Taitsukun lives on the enchanted Mt. Taikyoku where only the pure of heart can enter. She possess a mirror there that can see and remember all events in any part of the four kingdoms. Taitsukun is also attended by spirits called Nyan-Nyan (Chinese - girl). They can cure wounds and sickness and repair objects and, with their permission, ghosts can inhabit their bodies and become solid.
The Shijintenshisho: The "Book of the Four Gods of Sky and Earth" is a book that is in fact an incantation with the power to pull the mikos into the world of the four gods. Four copies of the book were given to the four different kingdoms by Taitsukun, one for each god. Taitsukun gave Suzaku's Shijintenshisho to Taiso, the first Emperor of Konan, with instruction for the miko who would someday come and find her seishi. The book (or scroll) is also burned in the ceremony of summoning after being read aloud by the miko. It goes like this:
"The four directions of the sky, by using the way, mind and goodness, please tell the protector of the (whatever direction), (whatever god). Now I will complete the words. From the sky to the earth, come to us physically through the four ultimates. Please, make extinct every kind of evil by using your godly power to protect us. Only one wish, please listen to this. (burn the scroll) Please, come down to us from the sky!"
The summoning ceremony: The ceremony in which the miko and her seven seishi summon their animal god (duh). The miko reads the above passage from the Shijintenshisho and asks the god to come down from the sky and takes his power into herself. By the god's power, she may make three wishes, crying "Kaijin!" (open, god!) to invoke her deity. One of her wishes is invariably for the safety and prosperity of her country.