How do substitute teachers join social security?

You can ask to pay social security fees. According to "Guiding Opinions on Properly Solving the Problem of Substitute Teachers in Primary and Secondary Schools" (EC [2011] No.8):

4. Incorporate into social security according to laws and regulations. It is a very important and key measure to solve the social security problem of dismissed substitute teachers. According to the policy and direction of the national social security system reform, fully consider the actual contribution of substitute teachers, and incorporate them into the social endowment insurance for urban and rural residents or the basic endowment insurance and basic medical insurance for urban enterprise employees according to different situations. For qualified substitute teachers, they can enjoy urban and rural minimum living security and urban and rural medical assistance in accordance with state regulations.

Further reading: How to buy insurance, which is good, and teach you how to avoid these "pits" of insurance.