Answer by taking a quote from the following article:

Richard of Bordeaux was the younger son of Edward, the Black Prince, and Joan of Kent. Edward, heir apparent to the throne of England, had distinguished himself as a military commander in the early phases of the Hundred Years' War, particularly in the Battle of Poitiers in 1356. After further military adventures, however, he contracted dysentery in Spain in 1370. He never fully recovered and had to return to England the next year.

It is only with the Peasants' Revolt that Richard starts to emerge clearly in the annals. One of his first significant acts after the rebellion was to marry Anne of Bohemia, daughter of the Holy Roman Emperor (King of Bohemia Charles IV) and his wife Elisabeth of Pomerania, on 20 January 1382. The marriage had diplomatic significance; in the division of Europe caused by the Western Schism, Bohemia and the Empire were seen as potential allies against France in the ongoing Hundred Years' War. Nonetheless, the marriage was not popular in England. Despite great sums of money awarded to the Empire, the political alliance never resulted in any military victories. Furthermore, the marriage was childless. Anne died from plague in 1394, greatly mourned by her husband.  Michael de la Pole had been instrumental in the marriage negotiations; he had the king's confidence and gradually became more involved at court and in government as Richard came of age. De la Pole came from an upstart merchant family. When Richard made him chancellor in 1383, and created him Earl of Suffolk two years later, this antagonised the more established nobility. Another member of the close circle around the king was Robert de Vere, Earl of Oxford, who in this period emerged as the king's favourite. Richard's close friendship to de Vere was also disagreeable to the political establishment. This displeasure was exacerbated by the earl's elevation to the new title of Duke of Ireland in 1386. The chronicler Thomas Walsingham suggested the relationship between the king and de Vere was of a homosexual nature, due to a resentment Walsingham had toward the king.  Tensions came to a head over the approach to the war in France. While the court party preferred negotiations, Gaunt and Buckingham urged a large-scale campaign to protect English possessions. Instead, a so-called crusade led by Henry le Despenser, Bishop of Norwich, was dispatched, which failed miserably. Faced with this setback on the continent, Richard turned his attention instead towards France's ally, Scotland. In 1385, the king himself led a punitive expedition to the north, but the effort came to nothing, and the army had to return without ever engaging the Scots in battle. Meanwhile, only an uprising in Ghent prevented a French invasion of southern England. The relationship between Richard and his uncle John of Gaunt deteriorated further with military failure, and John of Gaunt left England to pursue his claim to the throne of Castile in 1386 amid rumours of a plot against his person. With Gaunt gone, the unofficial leadership of the growing dissent against the king and his courtiers passed to Buckingham - who had by now been created Duke of Gloucester - and Richard Fitzalan, Earl of Arundel.

How old was he when he married Anne?
on 20 January 1382. The marriage had diplomatic significance;