Ibex hunt from Yemen, 0-300 AD
People seem to have lived in the Arabian peninsula from a very early date, perhaps crossing over the Sinai from Egypt. We don't know as much about these people as we would like to, because not very much archaeology has been done yet in the Arabian peninsula (modern Saudi Arabia, Yemen, Qatar, Oman, and the United Arab Emirates). But from what we do know, it is clear that these people had a thriving early civilization.
The south-western part of the Arabian peninsula 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 people built huge earthen dams across the streams to store up water for irrigation. We know that they also built big palaces, though not very much is left of their palaces now. The Queen of Sheba who is mentioned in the Bible as having visited King Solomon in the 900s BC was probably the ruler of a kingdom in this area.
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In the north and the east, 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. 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.
For more about early Arabia, check out these books from Amazon.com or from your library:
Arabia and the Arabs: From the Bronze Age to the Coming of Islam, by Robert G. Hoyland (2001).