Multimedia packages are made available on many alternative repositories, often because of distributions restrictions on available codecs due to patents in some countries (mainly US for the moment).
Everything would be perfect in a wonderful world if package builders would contribute to official distributions, and multimedia editors chose only free codecs to promote their use worldwide ... So try to stick to distributions deliveries?
Most linux distributions provide recent binary packages of Kdenlive that can be installed from your Package Manager. However, in some cases you can find more recent versions in private repositories.
This page at the Kdenlive home has instructions on how to source these more recent versions depending on what flavour of Linux you run. Instructions for Debian, Fedora Gentoo, OpenSUSE, Slackware and Ubuntu are available.
The current stable release is version 0.9.6 released 7th April 2013.
Debian project ships Kdenlive packages since "squeeze" (6.0) release, however to benefit from recent updates and bugfixes you might consider upgrading to a "testing" release or even "sid".
Ubuntu also offers Kdenlive since "gutsy" (7.10), but for similar reasons it could be preferable to upgrade to the latest release.
In both cases a simple
apt-get install kdenlive should then work.
RPM packages are not yet maintained in official branch, so you must go through an unofficial repository such as RPM Fusion or packman. Follow the sites recommendations to make them available and end with
yum install kdenlive
Building scripts are ready for up-to-date systems, so run respectively
emerge kdenlive or
pacman -S kdenlive or
pkg_add kdenlive, etc.
Kdenlive and MLT can compile and run under Mac OS X. Packages are available from the MacPorts project.
MacPorts is a source-based system - there is not a binary app bundle for Kdenlive. Therefore, Kdenlive and all of its numerous dependencies including multimedia libraries, KDE, and Qt must be compiled. This can take a long time and much disk space! Furthermore, it is not unusual for something not to build correctly; it is definitely not something for the novice, impatient, or "faint of heart."
For more details see this
You may have some success getting support for the MacPort of kdenlive on the Mac Ports forum on MacOS Forge
If you want to test latest committed code or your personal patches, you will have to build Kdenlive (and probably MLT) on your own.
You can use your distribution's package building procedure to use its software management system to install/upgrade/remove the binaries and data, and eventually share your builds (and even contribute to package maintenance - refer to the respective distribution manual).
If you prefer you can build & install Kdenlive to a local area (preferably not /usr, but rather /usr/local or $HOME/my_local_builds/kdenlive-last-release or similar). It is then recommended to use the build script 
Olivier Banus (AKA Sunab) provides a personal package archive (PPA) of the latest development trees of Frei0r-plugins, MLT and Kdenlive. For details on how to install Kdenlive using this source see launchpad.net
Dan Dennedy provides automatic daily builds that contain the latest git versions of Kdenlive, MLT, Frei0r, FFmpeg and some other important libraries. You can test this packages without changing your system. Just download the package and extract it to a folder of your choice. Inside that folder is a "start-kdenlive" executable that will start for you the latest Kdenlive.
Execute this by typing ./start-kdenlive in a terminal
Daily builds are currently provided for Ubuntu (should be compatible with OpenSuse 12 and Debian 7) and Fedora.
See the daily builds rss feed which provides links to the builds for the above mentioned distributions.
See also Kdenlive homepage
ENABLE_SWFDEC=0in the config variables of the script