First of all, thanks for your interest in Wake-On-LAN and www.remotewakeup.com
To wake up a computer, you need a usual network card and a router which allows to recieve such packets. Every modern NIC (network interface card) PC should be able to recieve such packets.
The router has to be configured for recieving arriving packets from the internet. So the router can route packets from the outbound to the inbound side of your local net. Therefore a new firewall rule must be created.
We need to create a inbound firewall rule which will direct packets from the internet to the local site. Most common for Wake-On-Lan is port 9/udp. But you can feel free to use another port you like.
The router knows that he now can accept packets at the desired port, but the router doesn't know where to send the packets. Therefore you have to configure the Broadcast Address as the target, since the packets should be sent as broadcast to all available stations in the same ip range. In most cases it is: 192.168.xxx.255.
After the firewall rule was created you can test your WOL. You just need the MAC-Adress of the computer which should wake up and the IP or hostname of the router. To determine your MAC-Adress you may press the Start button -> Execute und enter cmd. Afterwards you recieve the information by typing ipconfig /all. There you find the MAC-Adress, which should look like this: 00-0C-6E-2E-5F-01
Note: To keep your external IP Adress in mind: Many routers support free services like dyndns. Thus you don't keep your IP Adress in mind - therefor you can use a hostname like for instance hostname.dyndns.com
Enjoy your WOL!