An internet connection is required for Control Center to function properly.
A hardwired network connection (ethernet) is typically more stable and thus preferred for Control Center to perform optimally. You can, however, also connect Control Center to an available wireless network.
If you choose to use a wireless network, just follow the on-screen guide during setup to select the network name, and enter the password (if required). Please be sure to select a wireless access point that is nearby with a strong signal. Weak signals can result in sluggish behavior and random connectivity failures.
Please remember that Control Center as well as all your source devices must be connected (wired or wireless) to select the same network. Control Center connects and sends commands to many devices over IP. If Control Center is connected to a different network, it will not be able to properly communicate with them.