Installing Debian is a fairly simple task and is distributed freely over the Internet. It is possible to install it in several ways: from a CD, DVD, USB drive or Blue-ray disk, over a network, bootstrapped from within another Linux distribution by using Debootstrap, or from a MS Windows system. After the initial installation has been completed, further upgrades and maintenance are performed using built-in package management tools. It's possible to upgrade major software components, or even transition between releases of Debian without reinstalling the system.
At any given time, there is one stable release of Debian, which has the support of the Debian security team. When a new "stable" version is released, the security team will usually cover the previous version for a year or so, while they also cover the new/current version. Only stable is recommended for production use.
There are also two main development repositories "unstable" and "testing" which are continually updated during the development of the next stable release. The latest packages arrive in "unstable" (which always has the codename "Sid"). Packages are automatically copied from unstable to testing when they meet criteria such as lack of release-critical bugs, and dependencies being satisfied by other packages in testing.
Prior to making any major change to your computer you should ALWAYS backup all of your work. While the Debian Installer has been extensively tested, it cannot prevent you from making mistakes nor a prevent a power failure in your city while you are installing your new operating system.
Select Appropriate Debian Release
Refer to Debian Releases for more information about the Debian versions, but the following ideas may guide your decision.
Choose Debian "Stable" if you want the computer to just work for a prolonged period of time, without the risk of new packages breaking your habits or workflow. In most cases, when people talk about Debian, they are referring to Debian "Stable".
If it is important to you to have recent packages of all the installed software continuously rolling onto through Debian, and you are fine with constantly downloading and installing updates that may stir up a bug every once in a while, you may choose Debian "Testing".
If it is important to you to have the absolute latest packages available in Debian, you should learn about Debian "Unstable".
Where do I get Debian?
There are two main choices of installation media to meet your needs.
1. Download the network install image
For those with broadband Internet access it is often preferable to use a minimal network install image, rather than download a full set of 650 MB ISO images. This network install ISO (called "netinst") contains just enough packages to install a basic Debian system. During the install procedure only the required packages are downloaded from the Internet, making it more efficient overall. A netinst iso image is around 180 MB.
If your wireless network card is not recognized by the installer you might consider doing the installation using a wired (ethernet cable) connection or installing using a different network card. In any case it may be preferable to install with a wired connection for bandwidth reasons or simply to defer wireless setup until after the initial installation.
If you have no way of establishing a network connection during the installation, then you will need to install using full installation CDs or DVDs.
You can download the network install image here.
2. Download the full "CD/DVD" image
These images are for those who need all available packages that are in the current "stable" release of Debian.
Although there are over 30 CDs (or 5 DVDs) in a full set, only the first CD or DVD is required to install Debian. The additional images are optional and include extra packages, that can be downloaded individually during the installation, or later.
You can checkout how to download CD/DVD images here.
Buy a set of CDs
The easiest way to install Debian is with a set of CDs bought from a vendor. There is a list of CD vendors:
Netboot via another Debian system
There is also the possibility to boot from another computer without needing to use CD/floppy media at all. All you need is a TFTPD and a DHCPD running on the install-from computer. This is called installing via "netboot".
PXEBootInstall - the manual for setting up a netboot server.
An updated installer that supports the newest hardware
DebianLive - Debian Live CD / DVD / USB
InstallFAQ - Including how to install unstable (sid).
FAI, Fully Automatic Installation
PackageManagement - Managing your system
Debian GNU/Linux Installation Guide (all architectures, stable branch)