I had to write this for my History as well.

Thomas Becket
Thomas Becket was born in c.1118 in Cheapside, London, to Gilbert Becket of Thierville and Matilda (with a familiar name of Roheise or Rosea) of Mondeville near Caen. Gilbert, a knight's son, had taken the trade of mercer but in London was a property-owner, living on his rents. They were buried in Old St. Paul's Cathedral. There is a story that Thomas's mother was a Saracen princess who met and fell in love with his English father while he was on Crusade or pilgrimage in the Holy Land, followed him home, was baptized and married him. This story has no truth to it, being a fabrication from three centuries after the saint's martyrdom and inserted as a forgery into Edward Grim’s contemporary (12th century) Life of St Thomas.
One of Thomas's father's rich friends, Richer de L'Aigle, was attracted to Thomas's sisters. He often invited Thomas to his estates in Sussex. There, Thomas learned to ride a horse, hunt, behave like a gentleman, and engage in popular sports such as jousting. Beginning when he was 10, Becket received a brilliant education in civil and canon law at Merton Priory in England, and then overseas at Paris, Bologna, and Auxerre. Richer was later a signatory at the Constitutions of Clarendon against Thomas.
Upon returning to the Kingdom of England, he attracted the notice of Theobald, Archbishop of Canterbury, who entrusted him with several important missions to Rome and finally made him Archdeacon of Canterbury and Provost of Beverley. He so distinguished himself by his zeal and efficiency that Theobald recommended him to King Henry II when the important office of Lord Chancellor was vacant.
Henry desired to be absolute ruler of his dominions, both Church and State, and could find precedents in the traditions of the throne when he planned to do away with the special privileges of the English clergy, which he regarded as fetters on his authority. As Chancellor, Becket enforced the king’s traditional medieval land tax that was exacted from all landowners, including churches and bishoprics. This created both a hardship and a resentment of Becket among the English Churchmen. To further implicate Becket as a secular man, he became an accomplished and extravagant courtier and a cheerful companion to the king's pleasures. Thomas was devoted to Henry's interests with such a firm and yet diplomatic thoroughness that scarcely anyone, except perhaps John of Salisbury, doubted his allegiance to English royalty.
King Henry even sent his son Henry to live in Becket's household, it being the custom then for noble children to be fostered out to other noble houses. The younger Henry was reported to have said Becket showed him more fatherly love in a day than his father did for his entire life. An emotional attachment to Becket as a foster-father may have been one of the reasons the younger Henry would turn against his father.
He achieved his final position of power as the Archbishop of Canterbury in 1162, several months after the death of Theobald. Henry intended to further his influence by directing the actions of Thomas, his loyal appointee, and diminish the independence and affluence of the Church in England. The famous transformation of Becket into an ascetic occurred at this time.
A rift grew between Henry and Thomas as the new Archbishop dropped his Chancellorship and consolidated the landed revenues of Canterbury under his control. So began a series of legal conflicts, such as the jurisdiction of secular courts over English clergy, which accelerated antipathy between the two great offices. Attempts by King Henry to foment the opinion and influence of the other bishops against Thomas began in Westminster in October 1163, where the King sought approval of stated royal privileges. This led to Clarendon, where Thomas was officially asked to sign off on the King’s rights or face political repercussions.
But Becket started to disobey the King in thing to do with the Church, like for instance. Henry wanted to try criminous clerks in the Kings courts instead of the Church courts. Becket said no. Henry got very, very angry. Becket was exiled to France.
Henry pursued the fugitive archbishop with a series of edicts, aimed at all his friends and supporters as well as Becket himself; but Louis VII of France received him with respect and offered him protection. He spent nearly two years in the Cistercian abbey of Pontigny, until Henry's threats against the order obliged him to move to Sens again.
Becket sought to exercise the prerogatives of the Church, particularly the weapons of excommunication and interdict. But Pope Alexander III, though sympathizing with him in theory, favored a more diplomatic approach. Differences thus arose between Pope and Archbishop and legates were sent in 1167 with authority to act as arbitrators.
Becket's firmness seemed about to meet with its reward when in 1170 the Pope was on the point of fulfilling his threats and excommunicating Henry II. At that point Henry, alarmed by the prospect, held out hopes of an agreement that would allow Thomas to return to England and resume his place.









Assassination



In June 1170, the archbishop of York and the bishops of London and Salisbury held the coronation of Henry the Young King in York. This was a breach of Canterbury's privilege of coronation. In November 1170, Becket excommunicated all three. While the three bishops fled to the king in Normandy, Becket continued to excommunicate his opponents in the church. Soon word of this reached Henry.


After these reports of Becket's activities, Henry is said to have raised his head from his sickbed and roared a lament of frustration. The King's exact words are in doubt, and several versions have been reported. The most commonly quoted, as handed down by "oral tradition", is "Will no one rid me of this turbulent priest?",[6] but according to historian Simon Schama this is incorrect: he accepts the account of the contemporary biographer Edward Grim, writing in Latin, who gives us "What miserable drones and traitors have I nourished and brought up in my household, who let their lord be treated with such shameful contempt by a low-born cleric?"[7][8] Many variations have found their way into popular culture. Whatever the King said, it was interpreted as a royal command, and four knights, Reginald FitzUrse, Hugh de Moreville, William de Tracy, and Richard le Breton, set out to confront the Archbishop of Canterbury. On 29 December 1170 they arrived at Canterbury. According to accounts left by the monk Gervase of Canterbury and eyewitness Edward Grim, they placed their weapons under a sycamore tree outside the cathedral and hid their mail armour under cloaks before entering to challenge Becket.[9] The knights informed Becket he was to go to Winchester to give an account of his actions, but Becket refused. It was not until Becket refused their demands to submit to the king's will that they retrieved their weapons and rushed back inside for the killing.[9] Becket, meanwhile, proceeded to the main hall for vespers. The four knights, carrying naked swords, caught up with him in a spot near a door to the monastic cloister, the stairs into the crypt, and the stairs leading up into the quire of the cathedral, where the monks were chanting vespers. Several contemporary accounts of what happened next exist; of particular note is that of Edward Grim, who was himself wounded in the attack.





The burial of Becket
This is part of the account from Edward Grim:
...The wicked knight leapt suddenly upon him, cutting off the top of the crown which the unction of sacred chrism had dedicated to God. Next he received a second blow on the head, but still he stood firm and immovable. At the third blow he fell on his knees and elbows, offering himself a living sacrifice, and saying in a low voice, 'For the name of Jesus and the protection of the Church, I am ready to embrace death.' But the third knight inflicted a terrible wound as he lay prostrate. By this stroke, the crown of his head was separated from the head in such a way that the blood white with the brain, and the brain no less red from the blood, dyed the floor of the cathedral. The same clerk who had entered with the knights placed his foot on the neck of the holy priest and precious martyr, and, horrible to relate, scattered the brains and blood about the pavements, crying to the others, 'Let us away, knights; this fellow will arise no more.'
Following his death, the monks prepared his body for burial. According to some accounts, it was discovered that Becket had worn a hair shirt under his archbishop's garments—a sign of penance. Soon after, the faithful throughout Europe began venerating Becket as a martyr, and in 1173 — barely three years after his death — he was canonized by Pope Alexander III in St. Peter's Church in Segni. On 12 July 1174, in the midst of the Revolt of 1173–1174, Henry humbled himself with public penance at Becket's tomb, which became one of the most popular pilgrimage sites in England. In 1220, Becket's remains were relocated from this first tomb to a shrine in the recently completed Trinity Chapel where it stood until it was destroyed in 1538, around the time of the Dissolution of the Monasteries, on orders from King Henry VIII. The king also destroyed Becket's bones and ordered that all mention of his name be obliterated. The pavement where the shrine stood is today marked by a lit candle. Modern day archbishops celebrate the Eucharist at this place to commemorate Becket's martyrdom and the translation of his body from his first burial place to the new shrine.