First create a new group called something like "basic admin". Anyone added to this group is going to have access to a subset of the normal Admin functions.
In SysConfig, go to Framework -> Frontend::Admin::ModuleRegistration
In here you should be able to recognise how each module equates to the admin areas you will have been used to using. The easiest ones to give access to are Customer and Company as, in OTRS, these appear in the main menu, alongside "Dashboard" and "Ticket".
For each one, in the Group section at the top, click the plus button and add "basic admin". This gives users in that group read/write access to that module.
For any other modules, i.e. those that are only accessible by clicking on the "Admin" button, you need to make the Admin button available first. The safest way to do this is to give read-only access to the Admin Module itself:
Do this by clicking the plus button under Group ro: for this module.
Then proceed to grant read/write to any other remaining modules, such as:
OTRS 3.2.11 on Centos 6.4 with MySQL 5.0. Agents and internal customers authenticate via Active Directory.