Synaptic enables you to install, upgrade and remove software packages in a user friendly way. This may be the package management tool of choice for those who prefer a graphical user interface over using a command line. It provides roughly the same functionality as the command line package management tools.
The easiest way to run synaptic is from the Applications menu for your desktop environment. It may, for example, be in the Administration or System or Settings sections as the case may be. After launch, a pop-up dialog will ask for an administrator password.
Alternatively, you may run synaptic from a terminal using the command sudo synaptic, which also will prompt for the administrator password.
Installing, removing packages
Synaptic shows you all the packages available to you - and marks each one as installed or not installed. A green check box means the package is already installed. A blank checkbox means the package is not installed. (Help -> Icon Legend explains all the ways the checkbox can look.)
To find a package, use the search box or Ctrl+F to search packages by name, description, or other keywords; or just browse the package list by category. Users may also be interested in installing the apt-xapian-index package, which will add a convenient "Quick filter" search box to synaptic.
After packages of interest are found,
Mark packages you want to install (or remove) by clicking their check box, or by clicking them with the right mouse button and selecting Mark for Installation (or Mark for Removal)
Click the Apply button.
You can also decide to select Mark Recommended/Suggested for Installation to install recommended/suggested packages which may provide additional functionality for to the main package.
Upgrading all installed packages
Updated packages (minor upgrades or security upgrades) are regularly added to Debian repositories.
If no automatic upgrade mechanism is configured, you can use synaptic to keep your packages up to date:
Click on Reload to download new package information
Click on Mark All Upgrades
Review the list to make sure these are upgrades you are comfortable with, then click Mark in the pop-up dialog, otherwise click Cancel.
If you have selected upgrades, click Apply in the main window then in the pop-up dialog click Apply to upgrade all packages to latest versions.
This file can also be edited from synaptic. In the menu, click Settings -> Repositories
From there you can manage Apt repositories type, URL, distribution and components, which affect what packages are available to you, and the system upgrade policy.
Upgrading your distribution
See How to release upgrade your distribution to upgrade from one stable release to the next.