After enabling the Wake on LAN in the BIOS the operating system must be informed to enable it before the shutdown otherwise the machine will not turn on even if everything else is done properly.
To check if the network card supports the Wake On LAN then ethtool can be used:
# ethtool eth0 Settings for eth0: .... Supports Wake-on: pumbg Wake-on: d .....
If the Supports Wake-on field contains g then the Wake On LAN by magic-packet can be used:
# ethtool -s eth0 wol g # ethtool eth0 Settings for eth0: .... Wake-on: g .....
The command must be performed before the machine shutdown.
In the Apple OS X systems the Wake On LAN setting can be found in the System Preferences under the section Energy Saver.
On major Microsoft Windows OS the Wake On LAN is enabled by default so generally nothing to be done is needed. If the machine still doesn't turn itself on then you should check if the operating system has the Wake On LAN enabled with the magic-packet.
The following specifications can be different, they depends from the used driver.