How to attract vault members?

There are multiple ways to get more Shelter Dwellers:

- Lunchboxes

There is a chance to get a new dweller every time you open one of those boxes

- Make Babies

You can assign a male and a female dweller to the Living Quarters, now it's all about the honey and the bees, after a short while your Female dweller will be pregnant. note Pregnant dwellers are less efficient and therefore produce fewer resources.

- Radio Station

As soon as you hit a population of 20, you can build a Radio Station; this will attract more dwellers to the vault. You need to assign high charisma dwellers to the radio station to improve the success rate.

- Explore the Wasteland

Many guides point out that exploring the wasteland has an effect in attracting more dwellers to the vault (I'm just mentioning this for a complete list, as I can't confirm this works.)

The safety of your vault actually plays into people wandering to your place, if people frequently die, or are frequently unwell, they are less likely to show up. Other ways of course are radio station, make babies (easiest) obtain powerful character via lunch boxes, and the rare chance to find a save a straggler in the wasteland