What distribution are you using?
Most free software in linux comes in so called packages.
There are two main package formats: Deb for all Debain based distributions and RPM which is used by Red Hat, Fedora Core and SuSE (and others).
Your distribution has a package manager with which you can install/deinstall software and it also shows the installs packages.
On debian based distribution it is apt-get (command line tool) and mostly synaptic (graphical tool).
For the others I don't the know the package manager.
Commercial software exists in packages or in tar.gz archives. The packages can be installed with the package manager and the tar.gz archives must be extracted to the right directories - where these are depends of your distribution and the software.
You should read the manual, it will explain the installation procedure.
How the Env Variables are configured also depends on your distribution.
How the License is setuped depends of your application. Look in the manual.
The applications can be lunched by using an icon in the start menu or on the desktop (like in windows). Or you have to start the application by typing a command in a shell. However, like in windows, you can create your own icons.