the internet gateway

If you are not using a built-in firewall you are probably using an Internet Gateway Device such as a Linksys or NetGear.  You will need to setup Port Forwarding on the device to route requests to your computer.

Open a command prompt.  To do this press the Start button, click "Run..." and enter "cmd.exe" into the launch window and press enter.  In the command prompt type "ipconfig"

Note the information that comes back from IP config.  You will need it to configure your router. 

Open your web browser and enter the IP address of your default gateway into your browser.  This will bring up the web admin interface for your Internet Gateway device.  If prompted for a username and password, enter the appropriate information.  If you are using a Linksys, the default username is blank, and the password is "admin".

Next, find the port forwarding page.  It is usually under an "Advanced" tab.  The example below demonstrates how you would setup a Linksys router to allow Remote Desktop.

Specify the external port number (3389), the internal port number to route to (3389),  and select TCP protocol.  For the IP address, check back to your command prompt and enter the IP address of your machine, in this example 10.0.0.101.  Also be sure to check the "enabled" checkbox to turn on the forwarding.

Remember, ARD uses TCP and UDP ports 3283 and 5900.  Forward those ports, instead of 3389 if you run OS X.

This completes setup for your server.  Before closing your browser, find the status page of your gateway and write down the external IP address.  You will need this to connect your client.