Ubuntu 12.04 LTS is running a kernel from the 3.2 branch.
Newer stable kernel branches are 3.4, 3.5, 3.6 and the newest 3.7. Check the Linux Kernel Archives and the Linux kernel Wiki for the latest information about supported versions / branches.
When installing the latest kernel for Ubuntu, download it from the Ubuntu kernel-ppa/mainline. I used the v3.7.6-raring kernel (latest stable at the time).
Download 32-bit or 64-bit version of headers, image and image-extra plus headers-all file.
Open a terminal and execute : sudo dpkg -i linux-headers-3*.deb linux-image-3*.deb linux-image-extra-3*.deb
To uninstall as well as to remove un-use kernel, do following steps:
Boot up Ubuntu, launch Synaptic Package Manager (install it from Ubuntu Software Center) from the dash. Search for and remove following packages:
linux-header-x.x.x.x
linux-header-x.x.x.x-generic (possibly generic-pae or i686)
linux-image-x.x.x.x
x.x.x.x stands for the kernel version you want to remove or uninstall.
After that, run this in terminal (Ctrl+Alt+T):
sudo update-grub
Easy and without any pain !
Greetz, M.