Transmission

This sounds lame even to me.
After the download is complete, how do I launch the program?
Phoenix

Ok, let's go by parts. The program = Transmission or a program you've downloaded with Transmission? What is your OS?
Anyway, on Mac, you just move the Transmission icon to the Application folder and then double click it.
On Linuxes, it varies. For Ubuntu, follow the instructions here for proper installation (make sure to install transmission-gtk). For other linuxes, follow the instructions to build from a source tarball.
After Transmission is properly installed, either run "transmission" on a terminal window or click "Transmission BitTorrent Client" on the Application menu (Application>Internet>Transmission).