The short answer to this is, sometimes they didn't, really.

It was a great problem with the earliest colonists, and the first colonies. When the King granted land for a colony to someone like William Penn, for Pennsylvania, or Lord Baltimore, for Maryland, of course he had only the vaguest notion of the geography and so the grants were quite vague and not surprisingly overlapped. The results could be bizarre: Cecil Co Maryland overlapped land claimed by Pennsylvania, and right by land claimed by Delaware, and at one point in the 17th c. settlers thinking they had purchased land in PA and had built farms were informed by a Maryland landowner that they now owed their taxes to him, and he began to burn the hay of the ones who didn't pay. Though Cecil Co would soon get defined well enough for people to farm there undisturbed, setting all of the MD/PA lines properly would have to wait until 1763, done by the surveying team of Mason and Dixon: ergo the Mason Dixon Line.

Such vague grants were also turned to purpose. In 1649 Lord Fairfax was granted The Northern Neck, much of what's now northern VA and some of WV, defined as the land between the headwaters of the Potomac and the Rappahannock. But his descendant Charles only allowed squatters to move in, wouldn't actually sell land. The VA governor, William Gooch, was impatient with this: maintaining that the Potomac started where it met the Shenandoah, he began granting land above that point. Those grants were quite large, and the two families that got them, the Van Metres and the Hites, in turn sold it off to smaller farmers- and , even then, took the definition of their grants very loosely ( defining , say, 200 acres as being only the 200 acres around a rocky hill, but not including the hill.) Fairfax actually had to travel to Virginia from England in 1737 to try to deal with it, hiring a young and talented surveyor named George Washington ( who would end up liking the area and scouting for land for himself, as well). Like the MD/PA dispute, this boundary problem lasted decades. There would be various acts by the VA legislature and the English parliament over the matter until it was finally settled in Fairfax's favor in 1785.

When new land opened up to the West, after the Revolution, the problem repeated itself in Kentucky. Not, this time, by royal grants, but by speculators. Swarming into Kentucky territory after the armistice, they began scouting for good farmland and were filing claims for it almost before the Treaty of Paris was signed. There was no state-appointed or licensed surveyor, and , once again many claims overlapped. Lands were sold to settlers- or sometimes, other speculators. Sometimes, when the settlers actually arrived to take possession, they discovered that squatters had already arrived- and had to be removed. That happened to John Fitch, the steamboat inventor. He was one of these speculators, filing claims and then going back to Philadelphia to build a steamboat. After his steamboat venture failed, he returned to Kentucky and found not only that much of his land had been taken by overlapping adjoining claims but that it was also being farmed by squatters. He got a room at a local tavern and joined the long line of landowners who were filing lawsuits. He died before he was able to reclaim it. According to one account , Westcott's, he slowly signed away his claims, piece by piece, to the tavern owner to pay for his lodging, food, and drink.

For the Great Black Swamp and Ohio: Ohio was part of the territory included in the Northwest Ordnance of 1787, and this law actually set more rules for ownership, grants, etc. . Overlapping claims seem to have become less of a problem. For the Swamp, it would therefore have been relatively simple- a surveyor would find the corners of adjoining properties that had already been surveyed, and from that define the outline of the acreage that a settler would have bought of the Swamp. Whether it would be at all fun for the surveyor to do the job is another question, of course. George Washington was not alone in surveying the Northern Neck; Thomas Lewis left a journal of his surveying expedition in 1746, and it was anything but a walk in the woods.

for the Fairfax grant, a good history is Stuart E Brown, Jr's, Virginia Baron

For John Fitch's sad last years, Westcott's The Life of John Fitch is a thorough if not completely reliable source.