In gNewSense, package management is handled using the Debian GNU/Linux package management system (gNewSense packages are usually from Ubuntu, most of which are ultimately from Debian). Package maintainers create source and binary packages for many programs, from a variety of sources; this means most programs can be installed or removed in a single step.
In GNOME, packages can be easily managed with the Synaptic Package Manager (found in System > Administration) or, to a lesser extent, with the Add/Remove program.
Using the package manager is relatively simple. The buttons in the top part of the Synaptic window does exactly what they say; Reload refetches package lists from the internet, Mark All Upgrades marks all packages that are ready to be updated, etc. The left column of the Synaptic window can be used to filter packages in various ways.
In Settings > Repositories you can add lists of packages to use with your system.
When looking through packages, you will often see both a libsomething and a libsomething-dev version of a library. You should only get the "-dev" version if you are planning to compile a program that uses that library.
Synaptic Package Manager has the ability to change program files, so you must enter your password in order to either add new applications or remove old.
See also
Using the command line interface to install and remove programs