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From the setup page (https://cast.google.com/chromecast/setup), it appears that it generates its own access point that you connect to.

This is how WiFi-enabled printers and bathroom scales work, too.

Does it mean that I have to disconnect from my home wifi and loose ability to google stuff during this process?

The power chord is a USB cable. My guess was that you set it up on your computer via USB.

google.com/chromecast/setup gives you a link to download a native computer app. Looks like it does some wifi search from the native app to "pair" and setup the device.