This quest will not be available until after completing The Waters of Life. Once you have done that, return to Vault 101 (where you grew up) and tune in to the radio frequency on your PipBoy. You will find a distress signal from Amata. Head into the vault. From here you have a large variety of ways to finish the quest. I chose to simply convince her to stay in the vault. see the link below for all the options.
See Trouble on the Homefront for more specific info.
Note: This is your last chance to grab the bobblehead on your father's desk.
Caution: This may become unavailable if you load up DLC before completing it.