I have only recently started playing Fallout: Shelter, and so far I have 15 dwellers in my vault. I have a fairly good constant supply of power, food and water and the overall average happiness across my vault is 93%.
However, things just seem really slow considering that I haven't been getting many new dwellers in a while. Usually, I seem to be getting only about one or two per day.
Is this a fixed amount no matter what, or are there any ways of getting new dwellers quicker?
After the first 15 or so vault dwellers they stop showing up naturally, and you wont have dwellers waiting at your door until you build the radio station. At this point it's best to start breeding your existing dwellers until you have enough for the radio station. Once you build the radio station and assign dwellers to work it; they will attract more people to your vault.
Breeding
Put a male and a female dweller together in the residential area. If they're unrelated, they will (usually) hook up and the female dweller will become pregnant. It takes 3 hours before the baby is born and a further three hours before they become an adult. With the right breeding policy you can readily double your population in a day.
Note that pregnant dwellers will not fight, nor go to the wasteland, and that children eat and drink water but cannot work
In addition to the other two answer, I suggest you grow/breed your population as you can afford it, because falling below the water/food threshold can cause downward radiation poisoning cycle that takes a day or two to get out of. Also, try to build resting chambers on second or third level to the right side of your elevator since raiders (NPC's who will come to your vault to cause trouble) will visit your vault from top to bottom and left to right. I put my most well equipped dwellers on the first chamber they visit on the top floor so nothing to the bottom is affected.
