Windows "programs" are probably what you are thinking of. Their files end with .exe and none of them are usable.

Linux programs are called packages, and end with .deb. These are what you want. If you download a .deb from the web, you can then install it with a package manager. Doubleclick it and the package manager will open and ask if you want to install.

But, the easiest way is to not use the web at all. Linux distributions maintain lists of software, called Repositories. The default ones cover pretty much everything you need to touch, and you can add more if you want. All you need to do is run a command (as root), telling your package manager to install the software, and it will automatically grab the correct version (and keep it updated).

Here is an example, of me installing, and removing, the editor named 'emacs'

<pre> root@ubuntubox:~# aptitude show emacs Package: emacs
State: not installed Version: 45.0ubuntu1

root@ubuntubox:~# aptitude install emacs The following NEW packages will be installed: emacs emacs24{a} emacs24-bin-common{a} emacs24-common{a} emacs24-common-non-dfsg{a} emacsen-common{a} imagemagick-common{a} liblqr-1-0{a} libm17n-0{a} libmagickcore5{a} libmagickwand5{a} libotf0{a} m17n-contrib{a} m17n-db{a} 0 packages upgraded, 14 newly installed, 0 to remove and 23 not upgraded. Need to get 25.8 MB of archives. After unpacking 103 MB will be used. Do you want to continue? [Y/n/?] Y <a bunch of stuff is output here>

root@ubuntubox:~# aptitude show emacs Package: emacs
State: installed Automatically installed: no Version: 45.0ubuntu1

root@ubuntubox:~# aptitude remove emacs The following packages will be REMOVED:
emacs emacs24{u} emacs24-bin-common{u} emacs24-common{u} emacs24-common-non-dfsg{u} imagemagick-common{u} liblqr-1-0{u} libm17n-0{u} libmagickcore5{u} libmagickwand5{u} libotf0{u} m17n-contrib{u} m17n-db{u} 0 packages upgraded, 0 newly installed, 13 to remove and 23 not upgraded. Need to get 0 B of archives. After unpacking 103 MB will be freed. Do you want to continue? [Y/n/?] Y

root@ubuntubox:~# aptitude show emacs Package: emacs
State: not installed Version: 45.0ubuntu1 root@ubuntubox:~# </pre>