Security support for Debian 6 “Squeeze” reached end-of-life on 2016-02-29 ! Next LTS version is Debian 7 “Wheezy” :-)

To receive security updates, change your /etc/apt/sources.list

deb http://httpredir.debian.org/debian/ wheezy main contrib non-free
deb-src http://httpredir.debian.org/debian/ wheezy main contrib non-free

deb http://security.debian.org/ wheezy/updates main contrib non-free
deb-src http://security.debian.org/ wheezy/updates main contrib non-free

deb http://httpredir.debian.org/debian wheezy-updates main contrib non-free
deb-src http://httpredir.debian.org/debian wheezy-updates main contrib non-free

Update your system repositories:

~# apt-get update

..............
...........
........
Fetched 12.5 MB in 44s (279 kB/s)

Reading package lists... Done
W: There is no public key available for the following key IDs:
9D6D8F6BC857C906
W: There is no public key available for the following key IDs:
7638D0442B90D010
W: There is no public key available for the following key IDs:
7638D0442B90D010

Found the solution on stackexchange forum.

~# apt-get install debian-keyring debian-archive-keyring

Install apt from Wheezy before upgrading your system:

~# apt-get install apt -t wheezy

Upgrade your system, and carefully check all debconf prompts and update configuration files as needed.

~# apt-get upgrade

Open a new terminal and use vimdiff to check differences between old file and new conf file. In my case I neeed to change your sudoers file, and change users line

~# vimdiff /etc/sudoers /etc/sudoers.dpkg-new

~# vi /etc/sudoers

    myuser  ALL=(ALL:ALL) ALL

Upgrade your system and remove obsolete packages

~# apt-get dist-upgrade

    Reading package lists... Done
    Building dependency tree       
    Reading state information... Done
    Calculating upgrade... Failed
    The following packages have unmet dependencies:
     initscripts : Breaks: nfs-common (< 1:1.2.5-3) but 1:1.2.2-4squeeze3 is to be installed
    E: Error, pkgProblemResolver::Resolve generated breaks, this may be caused by held packages.

Remove NFS common and install it again

~# apt-get remove nfs-common
~# apt-get install nfs-common

~# apt-get dist-upgrade

    ................................
    ...................
    ..........

    Fetched 189 MB in 52s (3613 kB/s)
    Failed to fetch http://httpredir.debian.org/debian/pool/main/p/p11-kit/libp11-kit-dev_0.12-3_i386.deb  
    Error reading from server. Remote end closed connection [IP: ...... 80]

    Failed to fetch http://httpredir.debian.org/debian/pool/main/m/mpclib/libmpc2_0.9-4_i386.deb  
    Error reading from server. Remote end closed connection [IP: ....... 80]
    E: Unable to fetch some archives, maybe run apt-get update or try with --fix-missing?

~# apt-get update --fix-missing
~# apt-get dist-upgrade

~# apt-get autoremove