By default domain users are not allowed to install printers (printer drivers to be exact) on domain computers.
You can create Group Policy Object that will allow users to install printer drivers and apply it to required users. This will allow users to connect to shared printers on your network, download and install drivers without asking for administrator’s credentials.
This policy setting does not affect the ability to add a local printer.
For instructions on how to allow users to install local printers see:
In Group Policy Management Editor go to:
Computer Configuration -> Policies -> Windows Settings -> Security Settings -> -> Local Policies -> Security Options
and change Devices: Prevent users from installing printer drivers setting to disabled.

