First you need to talk to Socket and unlock the ability to buy cell upgrades. Then you have to but the first upgrade which will allow you to store one slave.
When you encounter a new character (inmate) you will be able to enslave them, it will give you a list of tasks. Then you have to complete these tasks. After doing the deed you will be able to kidnap them as you leave.
You can buy collars from the underground once you defeated Avy to enlsave other characters that are not inmates.