Tulsidasji has included this story (also found in other purans) in Ramcharitmanas also. I hope Sita11, if she is still on the forum, can post the dohas 48-103 which is where the story of Shiv and Sati is told. It looks like Tulsidasji wrote this story at the beginning of Ramcharitmanas.
Sati is actually the Divine mother or Shakthi who took the human form of Sati and was born as King Daksha's daughter. Daksha was a prajapati (mind born son of Brahma) and very arrogant. Sati also had another name Gauri because she had the golden color of tumeric or fair skinned. Sati was also called Daakshayini because she was the daughter of Daksha.
King Daksha wanted to marry her off to some great king but Sati wanted to marry Shivji. She knew that Shivji lived the life of an ascetic and decided to do tapasya to reach Him. She goes to the forest, against the wishes of her father, to do tapasya. There she lives the life of an asetic. In the course of her tapasya she lives on only one bilva leaf a day. Later on, she gives up even that bilva leaf and fasts; all the while doing pooja to the Shivling non stop. Because she gives up eating altogether to attain Shivji, Sati is also called Aparna.
Shivji is pleased and decides to marry her. Daksha is angry, because his daughter went against his wishes and married an ascetic like Shivji, and cuts her off from the family. He does not like Shivji and he is always insulting his son-in-law.
When Daksha performs the yagna he is supposed to honor all the Gods. He refuses to honor Shiva. Sati wants to go to the yagna. Shivji tells her that they are not invited and they should not go. Sati insists that she should go because invitations are not necessary between family members. Shivji is upset but does not forbid her. He refuses to go with her. Sati goes to her father's yagna and insists that her husband be honored in the yagna. Daksha is very rude to his daughter and tells her that he will not honor Shivji and he also asks her to go back.
Sati gets very angry at the insults of her father and decides to stop the yagna. She jumps into the sacrificial fire of the yagna. When she jumps into the fire, the yagna becomes impure and the yagna is stopped. Shivji becomes very angry at the loss of Sati and creates Virabhadra and Badrakali to destroy all the people at the yagna. The 2 ferocious creatures create havoc at the scene of the yagna. Shivji cuts off the head of Daksha.
Shivji is then supposed to have carried the charred body of Sati on his shoulders and does the raudra (angry) tandava dance. Since this would destroy all creation, the devas ask Vishnuji to intervene. Vishnuji uses his Sudarshana Chakra and cuts up the charred body of Sati into many pieces. The pieces of the charred body fall into the earth. The pieces where her body fell are considered Shakti peets and they have become pilgrimage centers. When this happens Shivji cools down. He then forgives all the people at the yagna and restores them to life. Even Daksha is restored to life and he is made the king again.
Before she jumps into the fire, Sati prays that she should be reborn again to a father who is worthy of her respect and not to a person like Daksha. In the next birth, she is reborn as Parvati (I think this means "of the hills" or something similar). She is called Parvati because she is the daughter of Himavan who himself is a great Shiv bakht. So, she gets a father she can respect in her next birth.
Sati, Gauri, Dakshayini, Lalitha, Parvati, Durga, and many many names are all different names for the same mother goddess we call Shakthi. Sati, Parvati, and such are just her human incarnations.
More to come...