The Debian package apt-howto is a good place to start with understanding the apt (for Advanced Packaging Tools) suite of tools. Once installed browse the file /usr/share/doc/apt-howto/en/index.html.
Also, see the Debian FAQ at http://www.debian.org/doc/FAQ/. In particular, Section 6 deals with the Packaging system. The Advanced Package Tool (apt) is the recommended way of managing packages under Debian. The command line interface is apt-get but it is also used within dselect, deity, and aptitude. See http://newbieDoc.sourceForge.net/system/apt-get-intro.html for a great introduction to apt-get. Also see /usr/share/doc/apt/offline.html/index.html on your local Debian machine for using apt off line.