fallenapples - There's a couple things to understand here. Windows and Linux are not the same. The .exe's you speak about are Windows only. Linux doesn't mess around with .exe's.
Additionally, Linux (Ubuntu in particular) uses .Deb packages to handle everything. These can be downloaded from Ubuntu supported web sites. For example if you go to Adobe's web site, you will see a Mac section, Windows, and Linux section, to which you can choose accordingly.
Linux has a package manager, which is actually a really organized way to handle everything you install. It's called synaptic package manager, available at system-administration-synaptic package manager. It'll ask you for your root password, type it in and fire it up. After that, you can search a large database of programs and applications to be installed on your system.
Example - Fire up synaptic and type in vlc. If you find vlc, right click it, install, and hit apply. Afterwards, VLC will automatically download and install on the fly.
You can also use add/remove programs as suggested above, which is how I might look to install VLC first. After you get familiar with it, synaptic is always there as well.