Open a terminal by pressing Ctrl+Alt+T, then type:
sudo apt-get install vuze
It will ask for your password, then will ask for confirmation.
Alternatively, click on the Ubuntu button (top left). Type
center and click on Ubuntu Software Center. There's a small search bar (on the top right), type
vuze. I guess you can continue from here.
Remark: These represent the recommended way for installing software in Ubuntu. Most of the time you won't need to surf the web to find the software you need, just open Ubuntu Software Center and search for it. This is one very nice feature.
(If your default language is not English, please specify so.)
For an introduction to Ubuntu 13.04 read the Ubuntu Manual. You can also visit the Ubuntu Guide (click on Packages to see an overview of how to install packages.