There are several ways to gain more Dwellers
The Radio StationRadio Studio is an option, but you need 20 Dwellers to unlock it,it; and when manned by low-charisma dwellers, attracting new Dwellers might take some time. Note that Charisma can be boosted with certain Outfits.
You can put two Dwellers together in your Living Quarters. Conceiving might take some time (note: the right Outfits also help here), as well as carrying the child and having it grow out to be an adult. There are however no pre-conditions for this approach, the outcome is pretty much guaranteed.
And lastly, you can send Dwellers into the Wasteland. Occasionally, your Dwellers will stumble upon a Red Rocket Truckstop, a Super Duper Market etc. Once in a while, there's refugees in there that want to join your Vault. Also, these explorers might find Outfits that boost Charisma, to help with the two points above.