Additional information will be required to assist you. What type of environment are you working in? Is it Windows, Linux, OSX, or NAS device? Do you have the database of users on Windows Active Directory? You can pretty much create a file server from a workstation, server, or network device but you will need to create all the usernames and passwords for the clients (users).
If this is a NAS box, create usernames and passwords that match the usernames the individuals use to login to their perspective computer.
There are two sets of permissions. One would be the share permission which allows the user to connect to the share. There are three types of share permissions: Full Control, Change, and Read.
The second set of permission is the folder permissions. Create folders with name of the user. You will give each user full permission to their individual folder.