First, just a note about re-installations. With Debian, a circumstance that will require a complete re-installation of your system is very rare; perhaps mechanical failure of the hard disk would be the most common case.
Many common operating systems may require a complete installation to be performed when critical failures take place or for upgrades to new OS versions. Even if a completely new installation isn't required, often the programs you use must be re-installed to operate properly in the new OS.
Under Debian GNU/Linux, it is much more likely that your OS can be repaired rather than replaced if things go wrong. Upgrades never require a wholesale installation; you can always upgrade in-place. And the programs are almost always compatible with successive OS releases. If a new program version requires newer supporting software, the Debian packaging system ensures that all the necessary software is automatically identified and installed. The point is, much effort has been put into avoiding the need for re-installation, so think of it as your very last option. The installer is not designed to re-install over an existing system.
Here's a road map for the steps you will take during the installation process.
Back up any existing data or documents on the hard disk where you plan to install.
Gather information about your computer and any needed documentation, before starting the installation.
Create partition-able space for Debian on your hard disk.
Locate and/or download the installer software and any specialized driver files your machine requires (except Debian CD users).
Set up boot tapes/floppies/USB sticks, or place boot files (most Debian CD users can boot from one of the CDs).
Boot the installation system.
Configure one network interface.
Open a ssh connection to the new system.
Attach one or more DASDs (Direct Access Storage Device).
Create and mount the partitions on which Debian will be installed.
Watch the automatic download/install/setup of the base system.
Install a boot loader which can start up Debian GNU/Linux and/or your existing system.
Load the newly installed system for the first time, and make some initial system settings.
Open a ssh connection to the new system.
Install additional software (tasks and/or packages), at your discretion.
If you have problems during the installation, it helps to know which packages are involved in which steps. Introducing the leading software actors in this installation drama:
The installer software, debian-installer, is the primary concern of this manual. It detects hardware and loads appropriate drivers, uses dhcp-client to set up the network connection, and runs debootstrap to install the base system packages. Many more actors play smaller parts in this process, but debian-installer has completed its task when you load the new system for the first time.
Upon loading the new base system, base-config supervises adding users, setting a time zone (via tzsetup), and setting up the package installation system (using apt-setup). It then launches tasksel which can be used to select large groups of related programs, and in turn can run aptitude which allows you to choose individual software packages.
When debian-installer finishes, before the first system load, you have only a very basic command line driven system. The graphical interface which displays windows on your monitor will not be installed unless you select it during the final steps, with either tasksel or aptitude. It's optional because many Debian GNU/Linux systems are servers which don't really have any need for a graphical user interface to do their job.