What HC said.
here's an example. Look at the shelf of my cabinet on my website. The center button in the middle of the shelf is my power button.
It's just a normal arcade buttons. If you open up a computer (as HC said, the modern computer, atx style) you will see the powerswith wires to the motherboard, not the powersupply. Also like HC said, computers have power management stuff now so directly turning off the powersupply like older computer is bad.
Also, to turn the computer off, you hold that button for X seconds. Though most new computer will automatically power down when you shutdown windows (if you use windows in your cabinet). Many pc monitors (if you use pc monitor in your cabinet) have an auto shutoff too. My monitor goes into a standby mode when the computer turns off.
Then you have computer cases like mine, AT/ATX compatible, it has both style switches, ahhhhhh.