1. Download the kernel’s source from http://kernel.org;

  2. Unpack it somewhere (will use ~/src/linux-3.11 here);

  3. Copy the config from the distribution over;

     cp /boot/config-3.8.0.30-generic ~/src/linux-3.11/.config
    
  4. Apply any patches;

  5. Go to the kernel source and create an up to date config.

     make oldconfig
    

    Just use the defaults for all the questions you’ll get;

  6. Compile the kernel into a debian package for easy installation and removal.

     fakeroot make-kpkg --initrd -j 8 --revision 3.11custom kernel_image
    
  7. Install the resulting .deb file and reboot.

     sudo dpkg -i ../linux-image-3.11.0_3.11custom_amd64.deb && sudo reboot