Do you want to use the latest version of Iceweasel, also known as Firefox?
Then add the repository provided by the Debian Mozilla team and choose between release, beta and aurora version.

There is a version updated for Debian Jessie – How to use a recent version of Iceweasel in Debian Jessie.

First step

Add GnuPG archive key for mozilla.debian.net repository to the list of trusted keys.

$ wget -q -O - http://mozilla.debian.net/archive.asc | \
  sudo apt-key add -

Second step

Add wanted repository to the active APT data sources.

Release version

$ cat << EOF | sudo tee /etc/apt/sources.list.d/mozilla-iceweasel.list
deb http://mozilla.debian.net/ wheezy-backports iceweasel-release
EOF

Beta version

$ cat << EOF | sudo tee /etc/apt/sources.list.d/mozilla-iceweasel.list
deb http://mozilla.debian.net/ wheezy-backports iceweasel-beta
EOF

Aurora version

$ cat << EOF | sudo tee /etc/apt/sources.list.d/mozilla-iceweasel.list
deb http://mozilla.debian.net/ wheezy-backports iceweasel-aurora
EOF
Please choose and use only one repository. You can find a basic version comparison at the bottom of this article in the ending notes section.

Third step

Assign higher priority to the recently added repository.

$ cat << EOF | sudo tee /etc/apt/preferences.d//mozilla-iceweasel
Package: *
Pin: origin mozilla.debian.net
Pin-Priority: 501
EOF

Fourth step

Update package index.

$ sudo apt-get update

Fifth step

Verify assigned priorities.

$ apt-cache policy iceweasel
iceweasel:
  Installed: 31.2.0esr-2~deb7u1
  Candidate: 35.0~a2+20141017004001-1~bpo70+1
  Version table:
     35.0~a2+20141017004001-1~bpo70+1 0
        501 http://mozilla.debian.net/ wheezy-backports/iceweasel-aurora amd64 Packages
 *** 31.2.0esr-2~deb7u1 0
        500 http://security.debian.org/ wheezy/updates/main amd64 Packages
        100 /var/lib/dpkg/status
     24.4.0esr-1~deb7u2 0
        500 http://ftp.icm.edu.pl/pub/Linux/debian/ wheezy/main amd64 Packages

Sixth step

Initiate upgrade or install process depending on your needs.

upgrade browser

$ sudo apt-get upgrade

install browser

$ sudo apt-get install iceweasel

Ending notes

Project website

Please visit the Debian Mozilla team website for more information and repository wizard.

Version comparison

$ apt-cache policy iceweasel
iceweasel:
  Installed: 35.0~a2+20141017004001-1~bpo70+1
  Candidate: 35.0~a2+20141017004001-1~bpo70+1
  Version table:
 *** 35.0~a2+20141017004001-1~bpo70+1 0
        501 http://mozilla.debian.net/ wheezy-backports/iceweasel-aurora amd64 Packages
        100 /var/lib/dpkg/status
     34.0~b1-1~bpo70+1 0
        501 http://mozilla.debian.net/ wheezy-backports/iceweasel-beta amd64 Packages
     33.0-2~bpo70+1 0
        501 http://mozilla.debian.net/ wheezy-backports/iceweasel-release amd64 Packages
     31.2.0esr-2~deb7u1 0
        500 http://security.debian.org/ wheezy/updates/main amd64 Packages
     24.4.0esr-1~deb7u2 0