The source of this tutorial is sysadminslife.com¹⁾ and describes the update process in a compact form.

Before you start the update, you should definitely start a data backup. Ideally, create a snapshot or a hard disc image. (I will not go into the procedure here)

cat /etc/debian_version
6.0.7

apt-get update
apt-get upgrade
apt-get dist-upgrade

Adapt the file /etc/apt/sources.list as follows (if there are entries from third-party providers, these must also be updated):

deb http://ftp.at.debian.org/debian/ wheezy main
deb-src http://ftp.at.debian.org/debian/ wheezy main
 
deb http://security.debian.org/ wheezy/updates main
deb-src http://security.debian.org/ wheezy/updates main
 
deb http://ftp.at.debian.org/debian/ wheezy-updates main
deb-src http://ftp.at.debian.org/debian/ wheezy-updates main

apt-get update
apt-get upgrade

List the current kernel:

dpkg -l | grep linux-image

Sample output:

ii  linux-image-2.6-amd64        2.6.32+29   Linux 2.6 for 64-bit PCs (meta-package)
ii  linux-image-2.6.32-5-amd64   2.6.32-41   Linux 2.6.32 for 64-bit PCs

Here you have to remember the meta designation (amd64 or 686):

apt-get install linux-image-2.6-amd64

update-grub

apt-get install udev

apt-get dist-upgrade

cat /etc/debian_version
7.0

shutdown -r now

Be sure to check the error logs!