1. First step is to click on the Azureus link, go to the site, and download the program.
2. Once you have downloaded the program (recommended to download to desktop) install it just like you would anything else.
3. After Azureus is installed you are almost ready to get started.  Go to any torrent site on the Internet and search for what you want to download. TorrentTyphoon and TorrentSpy are my two favorites.  Just type in what you want, and it will come up with a list of files.
4. You now need to download one of these torrent files. Choose the one that best matches what you were searching for, and also one with a "healthy" rating - meaning it has many seeders.  Each site has a different method or page layout for their downloads, but it's all the same basically, just click the file, and save it to your desktop.
5. Ok, that should have taken about 1 to 2 seconds.  Now you have a torrent file.  Open up Azureus.  When it starts up you will notice a top window and a bottom one.  The top is your downloads, the bottom is your uploads.  drag the torrent file that you downloaded into the top box of Azureus.
6. At this point your all done, basically you just sit back and watch your download start.  It will show you all of the progress, and when it is completed it will automatically move down to the lower box to indicate that you are now sharing the file.  Find the directory that you file(s) saved to, and there you go.  The default directory is usually C:/Program Files/Azureus/    That's where you'll be able to find all of your finished files.
If you have any questions feel free to leave me a comment, and I'll respond as soon as possible.