From the desktop:

System > Administration > Synaptic Package Manager

From the command line:

Adding new package

> sudo apt-get install <package name>

Removing package

> apt-get remove <package name>

Removing package and All Configuration Files

> apt-get remove --purge <package name>

Updating your installed packages

> sudo apt-get update

> sudo apt-get upgrade

or

> sudo apt-get install <package name>

APT will consider your command to be an update and see if a newer version is available.

Searching for a Package

> apt-cache search <package name>

To search only in the package names

> apt-cache -n search <package name>

To show more information about the package

> apt-cache showpkg <package name>

Cleaning Package Cache

APT maintains a package cache where it stores .deb files it has downloaded and installed. This lives in /var/cache/apt/archives, and can take up many disk space on your computer.

To delete all the cached .deb files

> apt-get clean

To delete the cached .deb files that are older than a certain, and only keeping newer packages

> apt-get autoclean

List Installed Packages

> dpkg --list