It depends a lot on which flavour ("distro") you're using, like Mandriva, Debian, SuSE, Fedora, and Slackware (and their variants like Knoppix, Gentoo, Ubuntu). It also depends a lot on the software - some has automated installers (similar to Win32's setup.exe) and some just give you the (usually c++) source code which you have to compile yourself.
If you're using Mandriva or Redhat Fedora, the automated installers are called "RPMs" (Redhat package manager). Or if you're using Debian (or Ubuntu), the "apt-get <application name>" system is what they use. Often, just double-clicking on the .rpm file is all that is necessary. Other times, you can spend a week trying to install a simple program and get caught up in "dependency hell" :Z
Your best bet is to join a forum like linuxquestions.org and poke around there.