Is that a source tarball or a binary tarball?
If it's a binary tarball, you're probably doing it wrong. Open up the Synaptic Package Manager and check to make sure that the program is not already in there. Then check the download site to see if they offer a .deb file (Debian package) instead. Using one of these two methods will make your life much easier- it makes it much easier to uninstall, it will automatically install any dependencies, and it will pretty much be guaranteed to work properly on your system. If and only if that fails, extract the tar file (right click and choose extract). There should be a file in there for you to run. You should run that file. If there's a README file in there, read that first.
If it's a source tarball, you'll have to use the command-line. First, right-click on the .tar.bz2 file and extract it. Open up a terminal and use cd to get to the folder. So for instance, if the folder is on your desktop and it's called "myprogram", you'll enter the command
cd Desktop/myprogram
If you haven't compiled anything before, make sure that the build tools are installed by running
sudo apt-get install build-essential
You'll be asked for your password. Enter it. You won't see anything appear on screen, but it's still working. Press enter after you enter the password.
Now, run the following three commands. If there are errors, look to see what they are and try to fix them.
./configure
make
sudo make install