I hate to go off on a tangent but for medieval aristocrats hunting was a very serious business, and was nothing like the modern sport hunting. Hunting had two main purposes, producing meat, and honing those skills necessary for warfare. A hunt required planning, knowledge of the game, knowledge of the environment, ability to manage a group of men, ability to work from horseback in a high intensity situation, and familiarity with use of weapons (and the bloodshed that results in their effective use). Medieval aristocrats were incredibly avid hunters, and it isn't uncommon to hear of them spending half the year on the hunt.

Hunting developed the fundamental skill set of knighthood, and became a highly ritualized form of chivalry in and of itself. They had special names for everything, special horn calls, equipment, really codified every aspect of hunting. They also wrote books on the subject.

Probably the best known treatise on hunting in the medieval era is Livre de Chasse, or Book of the Hunt written by Gaston Phoebus, the Count of Foix in 1387 or 88. The oldest English language book on hunting is a translation, adaptation and expansion of Livre de Chasse by Edward of Norwich, the Second Duke of York (who died at Agincourt) called The Master of Game. This book has been often reprinted, including an edition with a forward by American President Theodore Roosevelt (himself an avid hunter).

There were three ways for an aristocrat to develop knightly skills: hunting, mock combat (tournaments) and actual warfare, and hunting was the one they usually spent the most time at, and started earliest. Young Knights facing their first combat against human opponents would have honed their skills in combat training but also would have been blooded first by killing boars and bears at close range with hand weapons. Mastering the rituals of the hunt was also critical, medievals used hunting to pass on traditional views of manly virtue in much the same way modern men use sports as a vehicle for teaching lessons that are expected to be applied in real life after. Hard work, preparation, fairness, loyalty, teamwork, all the modern sports metaphors are equally applied to hunting. Older men used the hunt to teach young boys how to act, and men who were strangers could observe each other on the hunt and learn what kind of person they were dealing with. The social aspect is evident, but this isn't a foursome golfing on a business trip, it's much deeper than that.

People on a hunt were constantly being observed and measured, particularly in royal courts where everything is political. If you were invited on a hunt with a medieval monarch it was a long term affair, you might be at it for months. People would check you out at all stages. What kind of equipment do you have. Is it high quality, does it look like you use it often, is it well tended, are you familiar with it. The same with your horses and hounds, both in quality (hounds were prized, and considered a suitable gift between monarchs) and in training. A man with excellent animals who were well trained would be noticed for such things. How you hunted was important as well, how you handle your horse in the forest, how you work with others, how well honed your skills are, how cleanly you make a kill, how you handle adversity, how you respond to danger. If you had sons of age their behavior on the hunt was a reflection on you and your house. A good man on a hunt is a good man to have on your side in any situation, a poor hunter isn't someone you can trust or count on.

To touch on some other parts of your question, big groups would hunt deer. Deer were much more prevalent in the medieval era, and large groups of hunters would use group tactics to hunt them. They didn't use bows as much as most people (and filmmakers) assume (Gaston Phoebus recommends anyone wishing to learn more about bow hunting travel to England, which is where they hunted that way). A typical hunt for a Hart involved using huntsmen to track the forest for a suitable animal. Once chosen, they would place dogs strategically along game paths in places most likely for the animal to pass. The dogs and groups of horsemen were coordinated by horn calls. Once a group of dogs had the hart they would course after it, followed by men on horse. When the Hart was run to ground it would be killed by one man using a sword. Then the carcass would be dressed. Another common way to hunt was to separate into two groups, and have one group use dogs to drive game towards the other.

All of this is pretty dangerous. Running around on horseback at (literally) breakneck speed in thick forests in order to stage confrontations with dangerous creatures with very capable defense measures like claws, tusks and horns meant there were sometimes casualties. This added to the excitement, and also helped build the image of an aristocrat as one who takes great risks and does so casually. The way the hunting party was organized was itself a social construct, with the members all having specific ranks and duties. There was also an element of chance though, you never knew whose hounds would get the game, or who would make the kill.

The breaking, or dressing of the carcass was an important ritual as well. Each animal was meant to be divided in a specific way, not only in how it was cut up but how it was divided out. This was another medieval social construct, with each getting a portion according to their station, their duties, and their contribution to the hunt. The King would receive a share, or the local lord, and other portions would be donated to the church and the poor. The division was mainly given by station, but the most successful hunters would gain trophies and better cuts, which illustrates that there was some social mobility available. A man who was particularly good at using weapons and fieldcraft would see some personal gain as a result.

In a typical hunting party the King and great lords would work with lower level aristocrats (knights) and peasant huntsmen. They would engage in hunting exercises that mimicked military campaign skills. And they would divide the fruit of their labors using strictly codified methods of apportionment. Then they would wake up the next morning and do it all again. Medieval hunting was the nobles training ground for warfare, the means they used to teach each other how to behave properly, and a constant reinforcement of their social structure. I think a lot of moderns, even historians pass over the constant references to hunting among medieval aristocrats as just references to recreational activities, but there was a lot going on in what was essentially a hunting culture.