How to install h.264 decoder?

In order to play H.264 encoded videos the corresponding decoder comes with the following library:

sudo apt install gstreamer1.0-libav

If you want the H.264 encoder, then

sudo apt-get install h264enc

will install H.264 in your system.

I think this is part of the package gstreamer-plugins-bad. If you search for this in Software Center it should show up. It might be that you have to activate the multiverse repository (start Software & Sources and tick the appropriate box for this).

After you have installed the package, Movie Player should be able to play the file.