Taking another Grepolis city can involve siege or revolt mechanics depending on the world. These systems are not interchangeable. Check the world information first, especially before targeting an active player or a ghost town.
Prepare culture and a colony ship
Expansion needs an available culture slot and the required research and colony ship. You also need enough land and naval force to meet the method’s conditions and protect the ship on arrival.
Coordinate timing and support
Scout the target, clear relevant defences and synchronize naval and land movements. In siege worlds, the colony ship’s safe arrival can begin a separate occupation phase; if it is destroyed, the attempt can fail. Exact steps depend on the world.
Read the culture guide, colonisation tutorial and battle guide.