Survivors are saved by finding them and escorting them back to the safehouse. Survivors are mostly messaged to your cellphone while others only appear at certain points throughout the game.
This achievement must be done in a single playthrough, as opposed to 'Data Miner' which is cumulative, although both can be done in a single run, if managed correctly.
It is possible to do this in your first playthrough, along with the storyline, but I recommend saving them for a different playthrough, along with the 'use all items on zombies' achievements.
A guide for gaining both achievements in one playthrough can be found here.
A few pointers about survivors:
The game only allows you to have 8 survivors at the same time during the game, so if a mission doesn't trigger, chances are you'll need to finish a few missions before they appear.
When a message is incoming for the area you're currently present, the message will not appear. Leave the area to trigger it.
Do not hang about in the safehouse waiting for calls, messages do not appear and you might miss out.
Do not leave your survivors behind a loading screen. They gradually lose health and will die eventually. Always wait at the door until all the survivors have a green door icon above their heads/avatar.
Check their avatars. If someone seems to be lingering, chances are they are cripple or they're being held by a zombie. A quick glance at the avatar will reveal it's condition.
If you happen to come across a psycho encounter while escorting survivors, cram them in a maintenance room or any room with doors that is zombie-free and close it.