To build TumbleGonk on Ubuntu 12.10 you will need a development version of SDL2 (and SDL2_mixer and SDL_image). There is currently no official package for Ubuntu so you will either have to install from source or use unofficial packages.
To add unoffical SDL2 development packages to Ubuntu 12.10:
sudo add-apt-repository ppa:pj-assis/testing
sudo apt-get update
sudo apt-get install libsdl2.0-dev libsdl2-image1.2-dev libsdl2-mixer1.2-dev
TumbleGonk uses libvpx to play the tutorial video so you will need the libvpx development files.
sudo apt-get install libvpx-dev
To build TumbleGonk you will need the usual development tools for C++ projects.
sudo apt-get install build-essential automake autoconf libtool git
Next get the source from git
git clone git://git.code.sf.net/p/tumblegonk/code tumblegonk-code
Finally configure compile and install
cd tumblegonk-code
autoreconf -i
./configure --prefix=/usr/
make
sudo make install