How to install the MPEG-4 AAC decoder and the H.264 decoder?

ubuntu-restricted-extras package allows users to install ability to play popular non-free media formats, including DVD, MP3, Quicktime, and Windows Media formats.

To install ubuntu-restricted-extras package:

1. Open a terminal by pressing Ctrl+Alt+T.

2. Run this command:

    sudo apt-get install ubuntu-restricted-extras
   

3. Alternatively, you can install the package via Software Center by launching it via Dash and searching the package and clicking on Install.

Also, try installing libavcodec54 libav-tools and ffmpeg with this command:

sudo apt-get install libavcodec54 libav-tools ffmpeg

EDIT: Ubuntu 20.04

In Ubuntu 20.04, you want libavcodec58 instead of 54:

sudo apt-get install libavcodec58 libav-tools ffmpeg

The other answers seems to work on older versions but today when I was installing the same on clean install of Ubuntu 18.04 using Peachy's answer I got lot of errors. Using these commands I installed that in Ubuntu 18.04 LTS successfully.

sudo apt install libdvdnav4 libdvdread4 gstreamer1.0-plugins-bad gstreamer1.0-plugins-ugly libdvd-pkg
sudo apt install ubuntu-restricted-extras

Note: In 20.04, libdvdread4 has been updated to libdvdread7, and in 20.10, it's now libdvdread8 (see Ubuntu packages for the current version).

Support to decode MPEG-4 AAC is provided by gstreamer1.0-libav and to decode H.264 there is ffmpeg:

$ sudo apt-get install gstreamer1.0-libav ffmpeg

For more information have a look at the Ubuntu Documentation.

Unfortunately none of these options seem to work on Ubuntu 16.04. I get a python 3.5 message for searching MPEG-4 AAC in one of the videos I try to play. None of the above fixing the missing codec.

A fine workaround is to install VLC:

sudo apt-get install vlc

(or from software center)

Update: found a fix:

sudo apt-get install gstreamer1.0-plugins-bad

This made sound work for Totem (Video)

Update: Try going to 'Software & Updates' and enabling the checkbox for 'Software restricted by by copyright or legal issues'. Then allow Ubuntu to update after clicking the close button. You should now be able to run:

sudo apt-get install ubuntu-restricted-extras

You'll also have to accept the EULA's terms and conditions before continuing.