I had the same confusion when moving from Windows. "Where's the installer executable to download and install?" I would ask.
In Ubuntu you've got a few other options, mainly the Software Centre (graphical) or a command-line installer like
apt-get. I like apt-get. Once you get used to it (and trust it), it is so much easier.
On the command-line, try this:
sudo apt-get install eclipse
Enter password, confirm the download (because it's ~200Mb), and it will get and install the application for you.
If you don't have an executable in your system, typing the name in the command-line will often give you useful suggestions of what packages to download. So if you're looking for javac, say, entering it will give you a number of package target names that contain the javac program.
When you want specific versions of applications, things get a little more involved. If you can track down the
.deb file you want, Ubuntu will recognise it as such and bring up the Software Centre installer screen if you double-click on it. If you have a tar file as you mentioned above, generally you extract it and then run an executable contained within it. But with tar files you may run into library compatibility issues.