Most ISPs block the default port that Azureus uses. So it is a good idea to change Azureus' port number to something other than the default port. Here's a brief walkthrough on how to do that.
In Azureus click Tools in the menu at the top of your screen. Then click the Options link in the menu that drops down.
In the menu tree on the left hand side of this window Connection should be selected. Pick a random port between 49152 and 65535. Then enter that port into the Incomming TCP/UDP Listen Port box. When you are done, be sure to click the Save button at the bottom of the configuation screen.
Please enter the port you chose for Azureus below.
Open a web browser like internet explorer or Netscape. Enter the ip address of your router in the address bar of your browser. In the picture above the address bar has http://www.google.com in it. Just replace all of that with the ip address of your router. By default the ip address should be set to 192.168.1.1.
You should see a box prompting you for your username and password. Enter your username and password now. By default the username is admin, and the password is admin. Click the Ok button to log in to your router.
Click the Advanced link near the left side of the page.
You should now see a new menu. In this new menu, click Virtual Servers.
We will list a series of lines here that will show you exactly how to forward the ports you need to forward. Azureus requires you to forward the ports you entered above. Go ahead and enter the settings shown above into the Virtual Servers menu and then click Add.
You should see another page of settings that need to be entered into one of the blank lines on your routers Virtual Servers page. Go ahead and enter those settings and then click Add.
And that is it! You are done!