Install the Dependencies
1. Uninstall x264, libx264-dev, and ffmpeg if they are already installed. Open a terminal and run the following (you can usually paste into a terminal with shift+ctrl+v). Copy and paste the whole code box for each step.
Code:

sudo apt-get remove ffmpeg x264 libx264-dev

2. Get all of the packages you will need to install FFmpeg and x264 (you may need to enable the Universe and Multiverse repositories):
Code:

sudo apt-get update
sudo apt-get install build-essential checkinstall git libfaac-dev libjack-jackd2-dev \
  libmp3lame-dev libopencore-amrnb-dev libopencore-amrwb-dev libsdl1.2-dev libtheora-dev \
  libva-dev libvdpau-dev libvorbis-dev libx11-dev libxfixes-dev texi2html yasm zlib1g-dev


Install x264
3. Get the current source files, compile, and install x264.
Code:

cd
git clone git://git.videolan.org/x264
cd x264
./configure --enable-static
make
sudo checkinstall --pkgname=x264 --pkgversion="3:$(./version.sh | \
    awk -F'[" ]' '/POINT/{print $4"+git"$5}')" --backup=no --deldoc=yes \
    --fstrans=no --default


Install libvpx (optional)
4. This is used to encode VP8 video. If you follow this step, add --enable-libvpx to the FFmpeg ./configure line in step 5.
Code:

sudo apt-get remove libvpx-dev
cd
git clone http://git.chromium.org/webm/libvpx.git
cd libvpx
./configure
make
sudo checkinstall --pkgname=libvpx --pkgversion="1:$(date +%Y%m%d%H%M)-git" --backup=no \
    --deldoc=yes --fstrans=no --default


Install FFmpeg
5. Get the most current source files, compile, and install FFmpeg.
Code:

cd
git clone --depth 1 git://git.videolan.org/ffmpeg
cd ffmpeg
./configure --enable-gpl --enable-libfaac --enable-libmp3lame --enable-libopencore-amrnb \
    --enable-libopencore-amrwb --enable-libtheora --enable-libvorbis --enable-libx264 \
    --enable-nonfree --enable-postproc --enable-version3 --enable-x11grab
make
sudo checkinstall --pkgname=ffmpeg --pkgversion="5:$(date +%Y%m%d%H%M)-git" --backup=no \
  --deldoc=yes --fstrans=no --default
hash x264 ffmpeg ffplay ffprobe


Install qt-faststart (optional)
6. This is a useful tool if you're showing your H.264 MP4 videos on the web. It relocates some data in the video to allow playback to begin before the file is completely downloaded. Usage: qt-faststart input.mp4 output.mp4.
Code:

cd ~/ffmpeg
make tools/qt-faststart
sudo checkinstall --pkgname=qt-faststart --pkgversion="$(date +%Y%m%d%H%M)-git" --backup=no \
    --deldoc=yes --fstrans=no --default install -Dm755 tools/qt-faststart \
    /usr/local/bin/qt-faststart


Adding lavf support to x264 (optional)
7. This allows x264 to accept just about any input that FFmpeg can handle and is useful if you want to use x264 directly. See a more detailed explanation by forum member qyot27.
Code:

cd ~/x264
make distclean
./configure --enable-static
make
sudo checkinstall --pkgname=x264 --pkgversion="3:$(./version.sh | \
    awk -F'[" ]' '/POINT/{print $4"+git"$5}')" --backup=no --deldoc=yes \
    --fstrans=no --default