Set or Edit Permissions on a List or Library in SharePoint

To set or assign permissions for a library or list, first navigate to the list or library you wish to use and select Document Library Settings (or List Settings) from the Settings Menu.

This will direct you to the Settings page for the list or library.  From this page  click Permissions for this document library from the Permissions and Management menu, this will direct you to the Permissions page where you can select Edit Permissions from the Actions menu. One important thing to note is that by default, all lists and libraries inherit permissions from the site and have the exact same permission sets. To edit the permissions this must be turned off and you will be prompted to accept this after clicking Edit Permissions (unless inheritance has already been turned off).

Once inheritance has been turned off you will be able to edit user permissions or remove users from the Actions menu, or add new users from the New menu.