See here How to quickly compile libx264

In order to quickly compile your FFmpeg with the support for libx264 library, you can type the following commands in your shell:

# cd /my/path/where/i/keep/compiled/stuff
# git clone git://git.videolan.org/ffmpeg.git
# cd ffmpeg
# ./configure --enable-gpl --enable-libx264
# make
# make install
# ldconfig

P.S. If you are using Ubuntu, you'll most probably have to use sudo for the last 2 commands, like:

# sudo make install
# sudo ldconfig