Azureus has a built in tracker to allow users to share torrents directly, rather than uploading them to an "external" tracker. This is called "hosting" and can be performed by selecting this option from the context menu on the "My Torrents" view.
Configure the details of the embedded tracker via the "Tracker" tab on the "Configuration" view. There is an "External tracker IP address" field that must refer to the external IP address of your machine. Note that if you are behind a firewall this may differ from your machine's local address. To help in this task there is a "Check Address" button here. If your machine's external address isn't fixed (e.g. your ISP regularly changes it) then this will interfere with your hosted torrents, as the "announce url" will need to keep changing. If this is the case then it is advisable to use a DNS redirection service, such as DynDNS.org, to assign yourself a fixed DNS name - refer to the site for details.
In order to host a torrent it must have the correct "announce url" defined in the torrent. It must refer to the url of the embedded tracker. Use the File Menu/ "create a torrent" facility to construct a torrent, selecting the "Use Azureus embedded tracker" option to ensure the correct announce url is used. Then open the torrent and select "host". You will probably want to seed the new torrent, at least initially, so start the torrent and navigate to the file/directory used to create the torrent when selecting the download location.
You will see on the tracker configuration dialog that there is a port associated with the tracker, default value 6969. If you have a router/firewall you will need to open this port up for incoming TCP connections, as you will have done for the peer transport ports (default 6881 to 6889).
The tracker also, if enabled, publishes the hosted torrents and statistics as a web page. This can be accessed by using the tracker's root url. For example,
http://127.0.0.1:6969/. Other users can then download the torrents directly from here (
http://yourexternalIP:6969/ ).