How did the Persian Empire rule such a large empire?

Answer 1

1. They divided the empire into satrapies (provinces) with Persian governors supported by sufficient troops to enforce their rule.
2. They set taxes at a non-exploitive level. After the defeat of the Persian invasion of mainland Greece, Aristides was appointed to assess the levy on the Greek cities in Asia liberated from Persian rule which Athens was organising into an anti-Persian league; he mostly used the Persian system because he considered it just.
3. They kept internal order and protected the peoples from external invasion. Each satrapy and people within it was required to meet a levy of soldiers and warships proportional to their capacity.
4. They facilitated control, commerce and communication by establishing Aramaic as the lingua franca (the language which later Jesus spoke), and set up a fast courier system with staging posts to ensure speedy transmission of messages and reports in their pre-electronic era.

By retaining the local rulership with provincial governors maintaining security and external protection.