when did the people start using the silk road

Do you mean the Silk Road on land or Maritime Silk Road? The Silk Road on the land was opened by Zhangqian during the Western Han Period. The Maritime Silk Road was formed during the Yuan Dynasty. As they were opened, people started to use them to transport goods.

The Maritime Silk Road in South China was already in use at the time of Pliny the Elder (23CE-79 CE) and the Roman Empire. It became much more important during the Yuan Dynasty (which ended in 1368 CE), but its origins are during the Han (206 BCE-220 CE).