When the United States declared their independence from Britain in 1776, you could say that the British Empire wasn't exactly thrilled about simply pulling a Frozen and "let it go." As we all know the British and their loyalist Torries that constituted a reasonable size of the population at the time, were convinced they would take the colonies back for the crown. They put up a good show for 5 years but it all came to an end at Yorktown, Virginia.
The year was 1781
The victory at Yorktown wasn't a cut and dry as having superior tactics or manpower, but a great deal of it had to do with deception. At the time the British controlled the Chesapeake Bay (hence, Yorktown) and also New York City harbor, in 1781 these were essential ports for trade and also military supplies.
When the French arrived in Rhode Island a coordinated effort was made to march their forces towards NYC all the while convincing even their own troops that a siege of New York was the only military objective. Simultaneously, the French Navy was standing in wait to destroy the relatively small amount of British ships that remained in the Chesapeake Bay near Yorktown since most of their forces were being relocated to NYC in preparation for a siege that wasn't actually going to happen.
Personally, i am a little bit in awe at the level of coordination that was required to pull this off because it is not like there were cell phones or radios and if anyone was just a little bit late it would have threw the entire plan off. Also, the whole "loose lips sink ships" cliche was particularly applicable in this situation since there was only a select few members that knew the real plan in order to thwart any would be spies in the ranks.
The ruse was a success, and when General George Washington and French commander Comte de Rochambeau arrived at Yorktown with their sizable army of 17,000 troops, the British were surprised to see such a large force.
Word reached New York City that the British had been bamboozled and they immediately sent their Navy led by Sir Thomas Graves but the American / French had another trick up their sleeves as the "coalition" had secured a rental Navy from the Spanish who sailed north and routed the oncoming British ships based almost exclusively on superior numbers.
While the siege didn't last a tremendous amount of time one the nasty elements of being on the receiving end of a siege is that you don't have access to additional supplies, and since the Americans and French had superior numbers and a seemingly endless amount of supplies, the defenses were always going to be overrun.
Construction on artillery trenches began on Oct 6th and by the 9th the bombardment began. Washington ordered that the cannons be fired day and night to prevent the British from rebuilding. On the 14th the artillery lines had advanced to what was previously British exterior positions, by the 15th the US / French forces had such dominant positions that they were having competitions with one another to see who could cause the most damage. At one point Washington discovered a large building that he suspected might be Cornwallis' residence and ordered fire from the cannons: Within minutes the structure was completely destroyed.
On the 16th Cornwallis ordered the remaining naval units to be scuttled to avoid capture and the retreat of his troops across the river, the hope being some would be able to flee to New York on foot to plan a counter attack. As fate did not seem to favor him at all, a squall prevented all but the first wave of escape boats from reaching the other side.
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This painting by John Trumbull commemorating the vicotry is 12 feet by 18 feet and hangs in the U.S. Capital building
On the morning of the 17th, the British initiated a cease fire and The articles of capitulation were signed on October 19, 1781.
British reinforcements actually did arrive, but not until the 24th and upon seeing Yorktown in shambles and also noticing they were outnumbered by 9 warships, they turned back instead of engaging.
While these articles of capitulation were not the official end of the war. The capture of Cornwallis (considered one of the best Generals in the British military) and his troops negatively affected morale in Britain, which was already faltering. Losing Yorktown also all but completely eliminated any presence the British had in the entire south of the country. Seeing all these factors at once convinced the British to begin negotiations to end the conflict.
The Yorktown Victory Monument stands in Yorktown, Virginia to this day honoring the 88 killed in the French and American ranks (I'm personally surprised that number is so low.)
The official Peace of Paris, which made the United States an independent country, wouldn't be signed until 2 years later on September 3rd 1783. However, following the defeat at Yorktown, there were no additional major battles that took place as it was relatively understood in Britain that this war was a lost cause.