Dasharath, king of Ayodhya, had 3 wives, and no children. Agni, the god of fire, arose from the flames and gave Dasharath a golden vase with nectar in it to give to his wives. The wives consumed the nectar and gave birth to Rama, the eldest, Bharat the youngest, and the in the middle were twins: Lakshman and Shatrughna.
Ravana abducts Sita.
When the princess had grown up some, the sage Vishwamitra arrived at Dasharath's court and asked that Rama and Lakshman be "lent" to him to help him rid his hermitage of the demons that were plaguing the ashram dwellers by defiling their sacrifices with blood and bones, and by killing them off. After the two princes successfully rid the ashram of the demons, the sage took them to the neighboring kingdom of Mithila to show them the swayamvar festivities of the Mithila princess, Sita, born of the earth. The king of that country had adopted Sita as his daughter and, after Sita had grown up, had declared that he would give her in marriage to anyone who could string the Great Bow of Shiva.
Rama meets Hanuman and kills Ravana. 
Bharat was not in Ayodhya when these events happened; he, and the fourth prince Shatrughna, wereaway holidaying at Bharat's maternal grandfather's country. They were summoned to Ayodhya in haste and, when Bharat learnt what had happened, he was furious. He shouted at his mother, refused to ascend the throne, and gathered the townsfolk around him to proceed to the forest and bring Rama back. Rama refused to return, stating his intention to serve his father's last wish by being an exile for the full 14 years. Sita and Lakshman decided to go with him.
Rama is crowned by Ayodhya. 
One day, a demoness named Surpanakha saw Rama and, being charmed out of her wits by his beauty, walked up to him and begged him to marry her. "I already have a wife", said Rama and pointed to Sita. Surpanakha flew towards Lanka (modern Sri Lanka), ruled by her brother Ravana, and complained. Enraged, Ravana vowed vengeance. He persuaded the demon Marich to disguise himself as a golden deer and wander near Rama's hut. When Sita saw the golden deer, she begged Rama to get it for her. When the brothers were out pursuing the deer, Ravana arrived, abducted Sita, placed her in his flying chariot, and flew through the skies to Lanka. When the princes, after having killed the golden deer and discovered it was a demon in disguise, returned to their hut, they found it empty and started to look for Sita.
During their wanderings, the princes came upon a group of monkeys who showed them some ornaments of Sita's: the monkeys had seen a beautiful lady crying and dropping her ornaments from a chariot in the sky that was being driven southwards by a demon. Among the monkeys was Hanuman, who ultimately located Sita's whereabouts to be in Ravana's kingdom in Lanka. Rama gained the help of the monkey chief Sugreeva, gathered a monkey army, marched southwards, built a bridge across the ocean, and crossed over to Lanka. Rama, after an epic battle, was then able to kill Ravana and finally free Sita.
Since the 14 years were over by now, Rama then returned to Ayodhya, was crowned king, and ruled the kingdom with great wisdom: no child died before their parents did, no door needed locks against robbers, no farmland lay barren, no tree went fruitless, and there was peace and prosperity all around.