You can increase your population by adding and upgrading Housing buildings. Some other buildings will also provide extra population, like Janine's Farmhouse. You can add as many Housing buildings as you like and aren't restricted to just one housing block.
You can check the size of your population by looking at the number in the top-left of the base builder screen - it looks something like 25/90. This means that your base currently has a population of 25 people, and it has a 'population cap' of 90. You can increase your population cap by adding and upgrading buildings like Farms and the Hospital.