To Make field Read only to a user or a group of users involved using Profiles
Admin | Site Settings | Security Profiles New Profile
Give the Profile a name you will recognise and in the Description field offer a description to help others understand the purpose of the "Profile".
Select the table you want to apply the profile to and press "save" this causes the list of fields to be displayed now alter the properties of each field to either Full Access, Read only or no access.
having saved this the profile exisits and needs to be applied to an individual.
Admin | User Settings | select the user
For each user you can select specific tables to apply a Table Security Profiles restriction, you will need to add the table that you just worked on above and the rule such as if record manager if this is also to apply and then add the profile you just created.