Tried first to bribe the rulers of the Greek cities to join them. This succeded with some of the cities.
They then invaded the rest to bring them under their control. They threatened to invade the cities from the sea, which therefore kept their armies at home protecting their cities, which allowed the Persian army to pick them off one at a time.
Those who did not submit concentrated their navies to defeat the Persian fleet so that it could not threaten their cities. Wit the threat to their cities gonee, they could then concentrate their armies and defeat the land forces of the Persians and their Greek allies.
Persian forces advanced through Greece. More cities defected to them and Athens evacuated ther city. The Greek attempt on the Persian navy at Artemesion, to eliminate the amphibious threat, failed. They withdrew to Salamis to try again and won.
The Persians, unable to protect their supply fleet had to send half their army home for the winter.
The following spring, with no sea threat to the cities, the Greek cities were able to unite their armies at Plataia and defeat the depleted Persian army and its Greek allies. The Persians went home, and the remainder of their fleet, lurking at Mykale in Asia Minor, was captured.