Certain Apple displays had integrated power switches for Macs; these usually had ADC or USB connections to control the computer. Not all Apple displays had this feature, no non-Apple displays did, and not all Macs supported these monitors.
If you do have one of these displays, you will have to find the manual for your particular display to set this up.
Much more popular were Macs that switched on from the keyboard and in turn controlled a monitor plugged into the power port on the back of the computer. The G3 towers all had such a monitor power port, and the standard keyboard that came with them included a power button.
Good answer "Technologist"!
"Seattlepainter"...like "Technologist" mentioned about the monitors...the "auto" turn on also worked with a "button" on the keyboard...which was sort of just as easy as the monitor idea you mentioned.
Also...on the older G3 & G4 desktops some of them had two power "ports" on the back of them.
One was a "female" port for the power cord which went to the wall socket. The second plug was a "male" port which was the connector for a special "female" fitting on Apple monitors ONLY...where one of Apple monitors cables got plugged directly into the computer's power supply (instead of plugging the Apple monitor into the wall socket), and the monitors other cable attached to the computers video port, or video card.
So this whole setup in older Macintosh's...with the:
- special Apple monitor power plug into the computer
- the keyboard with the "power" button on it
...gave the user some additional options in terms of turning the computer on...and how the cables between the computer & monitor were routed.
"Technologist" pretty much said the same thing...I just expanded with some extra details.
Hope this helps,
- Nick