Ibex hunt from Yemen, 0-300 AD
People probably first arrived in the Arabian peninsula about 60,000 BC, perhaps crossing over the Sinai from Egypt or going all around the coast in their small boats. Some went on to Iran and India, but others settled down where they were.
The south-western part of the Arabian peninsula (modern Yemen) gets more rain than the north or the east, and so people began farming there more than in the other areas. Even in this area, there isn't very much water, and so beginning about 1700 BC people built huge earthen dams across the streams to store up water for irrigation. (Was this a response to the drought about 2000 BC?) The people of Saba were rich enough to build big stone palaces. The Queen of Sheba who the Bible says visited King Solomon in the 900s BC was probably the ruler of a kingdom in this area. By about 750 BC, the famous Great Dam of Ma'rib, the biggest of them all, stored water for the whole region around the city of Ma'rib. In 500 BC, they made the dam even bigger, to store even more water.
In the north and the east of the Arabian Peninsula, most people did not settle down and farm, because there wasn't enough rain. Instead, they became shepherds, and herded sheep all around the peninsula, going from one grassy place where there was water to another. Mostly these people rode donkeys. Because they were always travelling around with their sheep, many of these shepherds also became involved in trade.
It turned out that the trade was a lot more profitable than the sheep were. People from Egypt and Syria always wanted to buy things from India, and people from India always wanted to buy things from West Asia, so there was always trade going on. Some of this trade went by sea, from India around the Arabian peninsula and then up the Red Sea, but other times traders crossed the Arabian peninsula with caravans of donkeys. At first they brought Indian cotton cloth, glass beads, cinnamon and pepper, Chinese silk, and Central Asian horses and knotted rugs. From Egypt and Syria, they brought linen and wool cloth, blown glass, ivory, dates, gold, and silver. The Arabians themselves produced perfumed incense - frankincense and myrrh - and sold great quantities of it to West Asia, Egypt, and Europe at high prices.
Around 500 AD, thanks to improvements in camel saddles, these traders began to use camels rather than donkeys to move their trade goods across the Arabian Peninsula. New trade goods appeared: Indian steel and sugar, Central Asian paper and Chinese porcelain. But there were more changes too: about the same time, Roman traders figured out how to sail down the Red Sea and around the Arabian Peninsula to India, and cut out the Arabian middleman; also more trade began to go further north, by way of Palmyra. Many men in the Arabian peninsula began fighting instead as mercenaries for the Roman Empire and the Sassanian Empire, who were always fighting each other. That brought in money. But at the same time, there was a catastrophe: after some centuries of slow decline, the great dam at Ma'rib became too old to keep up any more; too much silt had piled up behind the dam, and in 570 or 575 AD, the dam finally broke. There was no more water for the fields, and thousands of people had to move out of Yemen to find new land.
Does the combination of displaced people, mercenary soldiers who knew just how lame the Roman and Sassanian armies were, and plenty of money from trade help explain the rise of Mohammed and Islam? Yes.
Learn by doing: go visit a big dam near you and see how it works
Go on to the life of Mohammed
Arabia and the Arabs: From the Bronze Age to the Coming of Islam, by Robert G. Hoyland (2001).