Question

How did people live and trade in the Islamic world

Answer 1

Culture

Many Western musical instruments were copied from instruments that originated in Islamic societies, including the lute, the guitar and the violin. It is said that Spanish flamenco dancing was influenced by the rhythms of Arab music.

Trade

European noblemen bought goods that Muslim’s traded in – silk, spices etc – as the height of fashion. Western sailors adopted devices that had been refined by Arabs, eg the astrolabe, which aided navigation, and the triangular sail, which increased manoeuvrability. Without these Columbus would never have reached America.
The Muslim economy stretched much farther and was more sophisticated than the trade of Western Europe:

Muslim traders travelled as far as South Africa, China and Russia.
They traded in fine quality goods like silk, cotton, carpets, paper, ivory and spices.
Hoards of medieval Muslim coins with Arabic writing on them have been dug up by archaeologists in Sweden which was thousands of miles from the nearest reaches of the Islamic World at the time.

The Islamic world experienced huge migrations of people:

the Seljuk invasions from Central Asia in the 11th and 12th centuries
the Mongol invasions from central Asia in the 13th century

Also, medieval Muslim traders and warriors settled over a vast area of the globe, taking their religion with them.

Muslim Arab traders and warriors set up trading posts and settlements throughout the Sahara, down the east coast of Africa, into India and even in south-east Asia.
After the Mongols converted to Islam, they established a number of Muslim states in Iran, Central Asia and Russia. The Mongol state in Russia was called the Golden Horde.
The ghazi military commanders who conquered eastern Europe after 1350 were given land there as a reward.