As in Game of Thrones, it depends on the ruler in question. Game of Thrones is very roughly based on the Wars of the Roses and assorted medieval machinations, so many of the characters have analogues in real life. Tywin Lannister for example is personified by Richard Neville, 16th Earl of Warwick who fulfilled a similar role as Kingmaker and was pivotal in the victory of Edward IV in the Wars of the Roses. Robb Stark or the young Robert Baratheon are personified by Henry V, who led an army to France and decisively defeated a French army at Agincourt, becoming personally involved in the fighting. Brienne of Tarth finds her medieval equivalent in Joan of Arc. Dragons and the undead aside, the Seven Kingdoms provide a (fairly) faithful analogue to feudalism and medieval society with institutions such as an organised church with a head, military orders and feudal levy obligations.

With regards to your question about the real world, it again depended very heavily on the ruler. Most male noble children would recieve a basic military education, serving as a page in another noble household and recieving military instruction as a squire with the eventual aim of being knighted. Naturally not every ruler was a fully trained warrior; if a ruler was sickly as a child or became overweight/elderly/crippled once acceding to their title, then they would not take be expected to fight on the front lines of battle but would send a trusted vassal or their heir, such as the Battle of Poitiers, where the English army was commanded by Edward, the Black Prince, who was the heir to the throne. This was also a useful tool for giving the heir some experience in leadership and warfare before they became King. It's worth noting that while I'm speaking generally here there were always exceptions to the rule. King John of Bohemia for example was both blind and fifty years old when he took part in and was killed at the battle of Crecy.

Kings and other high ranking Lords were often in comparatively little danger in battle. They would be able to afford the best weaponry and equipment, would be defended by the most able soldiers in the army and would often be targets for ransom rather than death. Whilst battlefields were obviously not the safest of places, it was in the interests of both sides to keep the high ranking Lords alive. Capturing a Lord alive would require him to pay a ransom for his safe return. For example, french Captain Sir Bertrand du Guescelin had to pay 100,000 Francs ransom when he was captured by the English, and after the battle of Poitiers English soldiers almost came to blows over who would accept the surrender of the French King Jean II and thus recieve promise of his ransom (he was released to raise a ransom but was ultimately unable to pay such a high amount, so voluntarily returned to England where he died in captivity).

However, the life of a nobleman was not always safe on the battlefield. Indiscriminate fire from archers, siege weaponry or even primitive artillery (there are records of at least one English soldier being killed by cannon fire at Agincourt) could kill, and when fighting against peasant revolts, in a Crusade or Mongols in the East there was no guarantee of quarter. Henry V ordered the execution of his prisoners during the battle of Agincourt because he feared that they would take up arms and attack him from behind, and following the battle of Crecy, Froissart claims that 'the king of England was bitterly angry that they had not been held to ransom, for there were a large number of dead lords'. When a Lord did die in battle, his heir would take over. It was highly uncommon for an entire family line to be wiped out in one battle, as there were often younger sons left at home or distant cousins who stood to inherit (for a Game of Thrones example see Bran and Rickon being left in Winterfell or (book spoilers) Harry the Heir being the heir to Vale due to his distant relationship to Robin Arryn). In the case where there were absolutely no eligible heirs then the lands and titles would revert to the liege lord of the deceased. When this happened with a King, in the example of Edward the Confessor, who died heirless in 1066, there would be chaos and often civil war as competing Lords tried to press their claim on the vacant throne.

For a good overview of the Medieval Period I'd recommend The Two Cities: Medieval Europe 1050-1320 by Malcom Barber.

For Medieval Warfare in general either Medieval Warfare: A History by Maurice Keen or The Wars of the Roses: The Soldiers' Experience by Anthony Goodman

If you want to learn about the Hundred Years War, Jean Froissart's Chroniques is a widely read chronicle from 1326 to around 1400. The Battle of Agincourt: Sources and Interpretations by Anne Curry is an excellent investigation of the aforementioned battle.

This Telegraph Article whilst not scholarly suggests some Game of Thrones characters and their real life equivalents.