You must not have read the info at the link, because they explain it. You plug into the "control" outlet whatever it is that you want to use to turn things on and off with, like your receiver (or whatever). You plug into the "switched" outlets whatever you want to get power whenever the "control" device is turned on. So, you plug the power amp into one of the "switched" outlets, with its power switch on, and plug into the "control" outlet whatever you want to use as the master device to give power to other things. I plug my receiver into the "control" outlet, and my power amp into a "switched" outlet. Whenever my receiver is turned on, it gives power to the power amp, and whenever my receiver is turned off, it cuts power to the power amp. The switchbox has a sensitivity control, because, of course, many devices use a small amount of power even when turned "off". In the case of my receiver, this is so the sensor in my receiver can detect when I use the remote to turn it on.
The price of the device I am recommending is only $30.95 (plus shipping). It is sold to be used with computers, so that you can automatically shut off power to all of the peripheral devices when you shut off the computer, and turn on the power to them whenever you turn the computer on. I use one for that purpose, too.
Like most such things, they are cheaper when they are marketed for use with computers than when they are marketed for use with audio equipment. My guess is that this is due to the fact that many audiophiles will pay crazy amounts for things that sane people would never pay. Surge protectors (this device is also a surge protector) sold for computer use are generally much less expensive than surge protectors sold for use with audio/video gear. I recommend forgetting about surge protectors that are marketed to audiophiles, because they are grossly overpriced. Buy one designed for use with a computer instead. If it is good for a computer, it will be good for a stereo.