How did ancient Greece expand their territory?

Answer 1

The city-states of mainland Greece each had their area of agricultural land around them. Their need to expand was based on the increasing population which even their continuous wars could not control. So when a city became overpopulated - that is more people than its agricultural land could sustain, the surplus was loaded on a ship and sent of to form a new city elsewhere. Usually those selected were mainly from the non-propertied class, so these had the chance to become landholders abroad. It was also a way of getting rid of political troublemakers to lead the colonising expedition. They partly-displaced other peoples already living there.

In this way hundreds of Greek cities sprang up right around the Mediterranean, from today's Spain and France, Sicily, southern Italy, North Africa, Asia Minor and around the Black Sea. These colony-cities were expected to pay some loyalty to their mother-cities, however this sometimes broke down and ended in hostility.

Answer 2

by winning a war