Debian packages are available in the official repositories. You can check the Kdenlive packages versions here: http://packages.qa.debian.org/k/kdenlive.html.
Debian packages are available for the following architectures: [alpha] [amd64] [arm] [armel] [hppa] [hurd-i386] [i386] [ia64] [kfreebsd-i386] [kfreebsd-amd64] [m68k] [mips] [mipsel] [powerpc] [s390] [sparc]:
As root, type:
apt-get install kdenlive frei0r-plugins dvgrab recordmydesktop dvdauthor mkisofs
Upgrade to Debian Unstable
The last released version of Kdenlive is usually available within 10 days in Debian testing, but if you really want to get Kdenlive's current development version, you might want to upgrade to Debian unstable. Be aware that this is for experienced users only and might break parts of your system that are currently working. In Debian terminology, the word unstable indicates that packages are not yet in a stable release. You may experience problems with some recent packages. Make sure you understand what you are doing.
Under root account, add the following lines to /etc/apt/sources.list:
You may select mirrors in your country for faster download.
To upgrade to Debian unstable, as root type:
Debian multimedia packages
Do NOT use the debian-multimedia.org repository. The debian-multimedia.org domain has now been bought by a untrusted source, please remove it from your apt list!