Asia might be exoticized and romanticized in modern times, but many people have no idea what prehistoric Asia was like.
Humanity is thought to have begun in Africa. In the Paleolithic time period, around fifty to seventy thousand years ago, some Homo sapiens began to move to Asia. They began to spread out over the next thousand years, moving into areas like Japan, China, and India. They began to use handaxes and other primitive chopping tools around this time.
By forty thousand years ago, Asia was well-populated, and even Australia was populated by Asian migrants. Archaeological evidence of humans’ existence is sparse in these areas, since it was so long ago.
The more fertile areas were soon home to permanent settlements by 4,500 BC, as humans learned domestication of animals, including the horse. The horse was initially bred for meat, but soon began to be bred for transportation, agriculture, and warfare (pulling war chariots). They irrigated wheat and barley fields, and may have developed a form of writing.
China in particular is difficult to categorize with the three-age system of archaeology, because it produced a large variety of bronze goods for a long time and iron smelting technology was discovered earlier than other civilizations. Generally, the beginning of the Bronze Age is placed at 3,000 BC or so, during the Shang or Xia Dynasty. It continued until about 200 BC, when the Zhou Dynasty disintegrated. Areas of China that were more arid became home to pastoral nomads, who domesticated animals and used their byproducts (such as wool, dairy products, etc). Herds of horses, goats, sheep and camels were maintained, and these groups migrated to find new pastures each year. Tents called yurts and made of animal hides and wood were developed to accommodate about five people each in this nomadic lifestyle as necessary. Cities soon formed that dominated the markets for goods that nomads could not produce because of their lifestyles. Since the nomads had little of interest to city dwellers, they began to carry out raids rather than trading for these goods.
Japan is unique because their ages are also somewhat different. Human activity is first tentatively dated to 40,000 BC or so. Ground and polished stone tools were developed at approximately 30,000 BC. (Normally, they would be dated around 10,000 BC, which marks a significant and unexplained difference.) This time period was probably dominated by big-game hunters. By 10,000 BC, hunter-gatherers were surviving, and some cultures were highly developed. Some farmstead or aquaculture activity may also have occurred. Rice farming probably took over by 500 BC, and peasant farming was common in later centuries. Chiefdoms were probably common by this time, and by 400 BC, drastic changes occurred that marked some continental importing activity. Japan evolved into a nation-state, but not wholly controlled by the central areas of Japan by the time history began.
Korea was probably occupied by humans by 40,000 BC. Early Koreans were cave-dwellers or lived in nomadic shelters, and probably built hearths for warmth and cooking. They were hunter-gatherers, and are suspected to have lived and hunted in communities. Tools such as arrowheads and chipped-rock implements have been found. Pottery was also being made from 8,000 BC onwards. By 4,000 BC, polished stone implements were made, but little is known about this time period. Settlements were formed, and the economy evolved to include foraging and some cultivation of plants. Pit dwellings were formed, and clothing was worn that was woven from fibers and decorated with natural seashells and stones. Society progressed from self-sustaining clans governed by councils to gradually link clans by intermarriage. Rudimentary nature worship and belief in spirits also formed. The Bronze Age caused drastic advances, and rice farming began by 700 BC. Farming tools were formed from bronze, and the country formed into a kingdom. Agriculture was well-developed and a variety of crops were grown by this time too.
Prehistory of Asia is a broad topic, and demands more time to cover than some other regions, owing to the large area and number of countries; an overview of these three East Asian countries is a good broad perspective to begin with.