There will be Side OPs called 'Extract the Wandering Mother Base Soldiers'.
There are a total of 10 of these. You will unlock another one after a certain mission.
Here's a list of which Side OP unlocks after which mission:
Extract the WMBS 1: Mission 6
Extract the WMBS 2: Mission 8
Extract the WMBS 3: Mission 16
Extract the WMBS 4: Mission 20
Extract the WMBS 5: Mission 23
Extract the WMBS 6: Mission 31
Extract the WMBS 7: Mission 31
Extract the WMBS 8: Mission 35
Extract the WMBS 9: Mission 38
Extract the WMBS 10: Mission 38
A very useful trick into catching the soldiers is hiding/walking in a cardboard box, or playing 'Koi no yokushiryoku (Love Deterrence) from your iDroid. You can find this song during Mission 1. I do both at the same time, and it works perfectly. The soldiers will recognize Snake because of the song or the cardboard box, and will salute you, letting you fulton him away.
Every time you extract a Wandering Mother Base soldier, he will give you a Memento Photo.
After this, you need to head for the first Medical platform on your Mother Base, and to the second level. There will be a door where you can go into. This small hallway leads to another door, behind which is someone (I won't spoil who) will look at the photo and tell you some stuff about it. After you've shown a photo, you need to leave and revisit Mother Base before you can show the next, so it's best to show a photo every time you're at Mother Base anyway. After you've shown all 10 photo's the last, and 11th, will spawn in the small hallway on the wall. The trophy should pop after this.