How can I upgrade
ffmpeg to version 0.6 on debian-based operating system?
I'm using apt-get for installation and deb packages.
Debian currently carries ffmpeg versions 0.5.2 in stable (squeeze), 0.6.2 in testing (wheezy) and in unstable. There's also a 0.7 package in experimental. Ubuntu currently carries versions 0.5.1 in lucid (Ubuntu 10.04) and 0.6.2 in natty (Ubuntu 11.04), and 0.7 in oneiric (in alpha-testing).
If you're running squeeze, 0.5.2 is the newest version of the package for squeeze. Debian makes no promise that they'll always have the latest version of every software, and fact the very premise of the stable release is that program versions are not updated during the lifecycle of the stable release. Similarly, 0.5.1 is the newest version of the package for lucid, which is a long-time support release of Ubuntu (no package upgrades unless absolutely necessary).
The Debian multimedia repository currently has 0.6.1 for squeeze. Generally if you want more recent versions or more features in multimedia packages, you should use that repository.
In general, if you want more recent versions, you can try recompiling the source package from testing or unstable on squeeze. The dependencies look ok. (Also, you can find some backports of testing packages to stable in the backports repository, but there isn't one for ffmpeg at this time.) For Ubuntu, similarly, grab the source package from a more recent distribution and try recompiling; or look for a PPA; there are many offering ffmpeg (not all of them offer current versions, and some of the matches don't have