In the millennium known as Treta Yuga, Krishna appeared as the avatar Rama, the valiant king, setting the standard for heroism, morality, virtue, and good government. The story of Lord Rama is told in detail in the epicRamayana. Here's a short summary based on Shukadeva Goswami's account in Srimad-Bhagavatam, Canto 9, Chapters 10-11.
In His youth, Lord Rama accompanied His guru Vishvamitra and killed demons like Maricha, who were disrupting the sacrifices of the sages. After breaking the stout and strong bow Haradhanu in the contest of heroes, He won the hand of princess Sita in marriage. Following a series of fateful events, to obey the order of His father, Rama moved to the forest, accompanied by His brother Lakshman and wife Sita. There they lived in exile for 14 years.
During their stay they encountered many demons. After one incident, where a she-demon tried to assault Sita, Lord Rama cut off the nose of the demon Shurpanakha and killed her accomplices, the associates of Ravana. Thereafter, the demon king Ravana decided to take revenge and kidnap Sita, which was the beginning of his misfortune. The magician Maricha assumed the form of a golden deer. Rama went to capture the deer to please Sita. The magician imitated Rama's voice, distracting Lakshman. In the meantime, Ravana took advantage of their absence to kidnap Sita. When the brothers discovered that Sita had been kidnapped, they searched for her throughout the forest. They met an old eagle named Jatayu, who informed them that he had seen Ravana fly away with Sita.
The Lord established a friendly relationship with Sugriva, king of the monkeys. After organizing the military strength of the monkeys and going with them to the shore of the sea, the Lord bridged the ocean and attacked Ravana's capital, Lanka. Previously, Hanuman, the eternal servant of the Lord, had set fire to Lanka, and now, with the help of Lakshman, the forces of Lord Rama killed all the demon soldiers. Then Lord Rama personally killed Ravana.

The Lord delivered Sita from an Ashoka forest where she had been kept a prisoner, and carried her in a flower airplane back to His capital Ayodhya, where He was received by His brother Bharata and enthroned as King.
As ruler of the world, Lord Rama, the Supreme Personality of Godhead, performed various sacrifices, gave charity to the brahmanas [saintly people], and enlightened them from within the core of their hearts.
During the reign of Lord Rama everyone was religious and completely happy. The forests, the rivers, the hills and mountains, the states, the seven islands and the seven seas were all favorable in supplying the necessities of life for all living beings. All bodily and mental suffering, disease, old age, bereavement, lamentation, distress, fear and fatigue were completely absent. There was even no death for those who did not want it.
Lord Rama took a vow to accept only one wife and have no connection with any other women. He was a saintly king, and everything in His character was good, untinged by qualities like anger. He taught good behavior for everyone. He taught the general public by His personal activities. --Adapted from Srimad-Bhagavatam, Canto 9, Chapters 10-11.
Devotees of Krishna celebrate the appearance day of His avatar, Lord Rama, by fasting until sunset and increasing their hearing and chanting about the Lord's pastimes. You may want to read the entire pastime in the pages of Srimad-Bhagavatam, Canto 9, Chapters 10-11. Listen to the audio narration about the Adventures of the Great King Rama. Chant extra rounds of the Hare Krishna maha-mantra japa, while especially meditating on the holy name of Rama: Hare Krishna, Hare Krishna, Krishna Krishna, Hare Hare, Hare Rama, Hare Rama, Rama Rama, Hare Hare. [Find out more about this mantra...] The great sages say that the name of the Lord is non-different from the Lord, and that by chanting His name, we associate with the Lord and keep His company. By uttering the sacred sound of His name, you're calling upon Him, invoking His presence. So think of Lord Rama today. Read about him. Hear about Him. Chant for Him. Cook a vegetarian dinner in His honor. Offer it to Him with love and invite friends over to eat the prasadam, sanctified food.