Cities can be built with Settler or Engineer units. The building takes time - 9 movement points, i.e. 3 turns for an Engineer but 6 for a Settler. During that time the unit displays as a different icon but it remains a unit for purposes of defense and ZOC. If you click on it, you may be told that it is settling down.
Location must be on a tile that is capable of being irrigated, i.e. hill, tundra, plain, prairie, or grassland. (It is, however, possible to have cities on other terrains if they are start positions on a map.)
The resulting city has a population of 2. Ensure that it will be viable, i.e. that the central tile plus at least one other available tile will produce 4 food units. Growth requires 5 or more food.