Brief (to be removed)
apt-get (for Debian)
yum (for Fedora)
brew (for mac)
Every Linux distro comes with its own package management system, which is a program that allows you to download other programs off the Internet through the command line. If you need to install a program on Linux, for example OpenOffice, vim or git, 99% of the time it will be available on the default package manager. All software is verified securely before being put on any package management systems, which is one of the reasons why Linux is such a secure operating system in general.
The default package manager for most Debian-based distros (Ubuntu included) is apt-get. For Fedora-based distros (for example centOS) the default package manager is yum.
Installing a program with either of these is easy. Type:
sudo apt-get install <package>
or
sudo yum install <package>
to install the necessary package.
For more commands, including how to update and delete packages, see man apt-get or man yum.
You can install other package managers on your system, and often there are package managers for modules written in specific languages. For example npm is a package manager for Javascript modules, and pip is a package manager for Python modules.