During the game there are 4 opportunities to rescues a Civilian, these require you to take out the enemies in front of them and then clear the area, once cleared you can approach them in order to "rescue" them,
Civilian #1 - R-01, When you exit the house fairly early on you'll see the Civilian in the street, it's very hard to miss, you need to sneak up behind the Cyborgs and Ninja Kill them both, then once they are taken out you can clear the area in order to free this Civilian.
Civilian #2 - R-01, Later on in this mission you'll fight a Hammerhead (the helicopter) and immediately afterward there will be a Civilian, this is made much easier if you have an EMP but it's not required, however they do supply you one in the chest to your left so I highly suggest you just use it, you'll need to throw an EMP to the 2 Cyborgs, once you do that you just need to kill everyone in the area and free this Civilian.
Civilian #3 - R-03, When you cross over to the building which has a straight pathway (the one which the Slider will fly right at you), you need to sneak behind the Cyborg approaching you and Ninja Kill him from behind, from here throw an EMP at the 2 Cyborgs by the Civilian, like before kill all the enemies and free this Civilian.
Civilian #4 - R-05, The moment you find a GRAD, this is where it is, Ninja Kill the Cyborg on the top and run back (just in-case the GRAD spots you), throw an EMP at the Cyborgs (it doesn't matter if it doesn't reach the GRAD) and kill every enemy then free this Civilian.