There are several ways of getting new dwellers into your vault. One is by mating. Place one male and one female dweller in Living Quarters and wait for them to develop and make love. The only exception about this rule is that family members won't mate. (Of course, for pete's sake) The female dweller will become pregnant. Once this happens, you can return both parents back to work.
A pregnant dweller can't be sent out to explore, she can't help with the incidents (she'll run and hide in the Living Quarters should there be an incident), and she can't train to increase her stats. You have to wait for 3 hours before a kid is born (which you can name). You need to wait for an additional 3 hours for the kid to grow up to an adult. Kids are counted toward the population count and they also consume water and food. Like pregnant women, they can't help with anything and will hide in case incidents occur. They'll just wander around the vault and mind their own business.
There are no limitations as to how you can pair up your dwellers. If you want an alpha male to impregnate all women in the vault, that's fine. However, that will severely limit your options for future generations because of the family limitations. Be careful not to have too many children and pregnant women in your vault since you'll be in trouble during incidents and it may affect your resource consumption as well.