Enable iTunes Library Sharing and Home Sharing

As part of the steps to configure your server's iTunes library, you should configure both Library Sharing within iTunes Preferences and iTunes Home Sharing.  This is required to allow other iTunes instances and iOS devices to see your library.

Share your library on the network

To enable this, open iTunes interactively, eg via Remote Desktop Connection, and then select the Edit / Preferences menu.  Choose the 'Sharing' tab:
Follow the steps below:

Enable iTunes Home Sharing

You also should enable iTunes Home Sharing.  To complete this step, ensure you are still running iTunes interactively, and then choose the "Advanced menu / Turn On Home Sharing" menu.  The following screen will appear:
Enter your Apple ID and Apple Password into the prompt and click 'Create Home Share'.
Your server's iTunes library will now be available on your home network.