This guide is for both the population and the number of cities achievement, as they go hand in hand.
First, as usual, for minimal interference, have 1 novice opponent faction. However, use a medium or larger map to ensure there's enough room. Set wildlands to None to increase the likelyhood of airable land being available.
Go about playing the game, focusing on finding spots to found cities. Aim for spots with 5 food, or a minimum of 4. Found at least four additional cities to get the Expansionst achievement
Once the cities are built, focus on improvements that improve food yield from grain. As the cities level up first choose for them Towns to unlock more food improvements. Build gardens, granaries, and storehouses to increase food yield in that city. Build grocers, bakeries, and butchers to increase food yield in all cities. Build the Brewery in the city with the highest grain count. Once you have 3000 grain being produced in your cities, then its just a matter of waiting for them to grow. Build improvements that help with that, set production to growth, and wait.