Historical context of population growth
Population expanded significantly in the middle ages, between the low after the ravages of the Justinian Plague of 541-542 to the high middle ages peak of ~1300 before the Little Ice Age brought famine.
According to the Medieval Sourcebook (possibly the best thing on the internet), the population of Iberia went from 3.5->9 million, France 3->19 million, Germany 2->11 million, Italy 2.5 -> 10 million, etc. Obviously this involved breaking in a lot of new land.
Bringing land into civilization
There were several ways that new land was brought into civilization, but the primary problem was defense. States existed in these worlds entirely to control violence. Anyone could gather up a band of ruffians and rob whoever they wanted, so the organization of society was primarily dominated by the ability to protect whatever gains were made from farming the land.
There were two processes: opening up new farmland, and starting new cities. Farmland didn't really need cities to go along with it; the truly independent peasants would not have any sort of advanced, tradable materials: very little iron, mostly for weapons instead of tools, wooden tools and buildings, animals for traction, and nothing that needed to be bought from the outside. Especially in the pagan lands of eastern europe, this was the peasant's way, though it might be more accurate to call them tribesmen since they had more in common with the Roman-era 'barbarians' than the medieval villein.
Opening new farmland
For breaking in farmland in truly remote areas, these were the peasant/tribes to do it. This mostly happened on the very edges of Europe, like the Baltic coast, and European Russia. But at the end of the Middle Ages and even after into the 1700s, this process was repeating itself with the Cossacks in the Ukraine, an extremely fertile area that had been totally depopulated by centuries of nomadic warriors from the Golden Horde and Crimean Khanate. Read up on Cossack history to get an understanding of how a peasant society would organize itself outside of an established kingdom.
But in more civilized areas land expansion often came from or with approval of some person in power. Abbeys were particularly keen on opening up farmland, since monasteries tended to be build in remote areas and then start to turn the surrounding countryside to cultivation. Examples would be Clairvaux in France and Eberbach in Germany.
An alternate method was for an overpopulated village to get permission from the local lord to clear a section of forest and start a new village some miles away. In the early middle ages, when lords were poor and land was plentiful, this was generally supported by the nobility. By the high middle ages, when lords were rich and the damn peasants were traipsing all over the only good forests for hunting, this was discouraged.
Starting new cities
New town formation was catalyzed around 1000 AD by the opening up of trade routes. Christianization of the Vikings and the end of raids from the north increased trade in the North and Baltic seas. The slowing down of the pace of Jihad lead to more trade opportunities with the Muslim world, particularly in Italy. Eventually, the Reconquista and crusades provided more East-West contacts and increased trade further, spurring the long range trade routes and walled merchant towns of the high middle ages.
Whereas the expansion of farmland tended to benefit the lowest levels of nobility and clergy, town growth benefited the upper levels. Cologne and Magdeburg grew because of the safety provided by the authority of the resident Archbishops made them attractive places to do business. Cities like Augsburg, Nuremburg, and Hamburg got charters from the Emperor to protect their freedoms in exchange for a lump sum of money. Bordeaux, Rouen, and Orleans got a royal charter in France. The direct communication with the highest leige (called immediacy) provided financial benefits to the leige, who could use the money to hire mercenaries to centralize his Kingdom, and protection to the cities from local nobles and clergy.
A similar thing would happen in Eastern Europe. Whereas in Western Europe there were or had been existing settlements, in Poland, Ukraine, and the Carpathian basin, towns were founded where none had been before. As towns sprung up they sought the protection of the most powerful local lord with a Magdeburg town charter.
Answer to your question
So to answer your question more directly:
If a group of peasants were to start a new settlement in a remote area of an established kingdom, they would either a.) need to get the consent of a local lord or abbot who would serve as their benefactor and and provide protection from violence or b.) they would be pillaged into the earth.
Their village would be small, in the hundreds of people at most. Proper towns only developed where there was business to be done, and if you are settling in a remote area, that is unlikely to be the case. However, supposing the new settlers are able to open up a new trade route (say by building a bridge or opening a mountain pass that had previously be little used), a town could potentially develop quickly. In that case, the town would seek a charter from the highest leige to protect its rights.
