Unfortunatley, due the the available input options on the 23" Cinema Displays it is not possible to connect HDMI equipped devices to the Cinema Display.
From memory, the only available input on the 23" Cinema Display is DVI which is widely available on both PCs and Macs (via adaptors).
You may be able to find a converter which would allow connecting to HDMI devices to your display, but in my experiences, these converters deliver a bad experience.
For the price of the necessary converter it may be possible to purchase a cheap monitor with HDMI inputs.
Hope this helps,