depends on what distro you use. debian and Debian based ( ubuntu, linux mint, etc) use .deb files. Fedora, Opensuse use .rpm files. Both double click and install. If its a .tar.gz file it is usually the source and needs to be compiled, ( ./configure, make and make install ) from the command line.
The best way is to use the package manager of your distro. Debian and the like use Synaptic, Others use YUM and Arch Linux ( my favourite ) uses pacman. These are programs that search an online repository for the software and then download and install it for you. here are some links

synaptic - http://en.wikipedia.org/wiki/Synaptic_%28software%29

pacman - http://wiki.archlinux.org/index.php/Pacman

YUM - http://en.wikipedia.org/wiki/Yellowdog_Updater,_Modified

compile from source - http://www.tuxfiles.org/linuxhelp/softinstall.html

there are other ways but these are the main ones, others might tell you about them.
Oh by the way .exe is a windows file and dose not work in linux, ( i know about wine but this is not the place ).
Hope this helps and please consider linux.

all the best
Garfilth

Please refer to the discussion you created at http://www.linux.com/community/forums?func=view&catid=18&id=7011 so we can review your chosen distro and apps so we can guide you in the right direction.