A tin-glazed plate
It's easy to tell Islamic pottery from the pottery that came before, because it was just at the time of the Arab conquests (about 600-700 AD) that potters began to use metal-based glazes on their pots.
Tin-glazed bowl imitating
Chinese pottery, ca. 850 AD
This way of glazing pottery had been invented in West Asia during the Roman Empire, but Roman potters didn't use it very much. Glass glazes became much more popular during the early Abbasid empire, about 800 AD, as a way of imitating white Chinese porcelain. Traders were bringing Chinese porcelain west to sell in Baghdad, but it was very expensive - the local knockoffs were cheaper.
From around 1400 AD
Islamic potters then began to experiment with lots of different glazes, often painting one color over another, and sometimes firing the pottery more than once.
From about 1300 AD
When the Mongols conquered Central Asia and China in the 1200s AD, there was more trade between West Asia and China. Chinese pottery again became fashionable in West Asia, and a lot of West Asian pottery began to copy Chinese colors and patterns.
To find out more about Islamic pottery, check out these books from Amazon.com or from your library:
Eyewitness: Islam, by Philip Wilkinson and Batul Salazar (2002). 1. For kids - the religion and culture of the Islamic Empire, with lots of pictures.
Pottery of the Islamic World: In the Tareq Rajab Museum, by Geza Fehervari (1998). A good representative collection, with many outstanding pieces, well illustrated.
Pottery of the Early Islamic Period, by Charles Wilkinson (1974). Relies on the collection of the Metropolitan Museum in New York.