You can increase your population by building more residential buildings. If you don't have enough free space in you city - try researching new, better residential buildings and building them instead of the old ones.
Each era has different types of residential buildings, which either grant more population or produce more coins. You can unlock them in the Research Tree. They're also some Great Buildings, which grant you more inhabitants, like the Tower of Babel, the Capitol or the Innovation Tower.
If you increase your population too much without having enough Happiness, it may happen, that your inhabitants become unhappy. So make sure, that you always have enough Happiness.