The first stable version of Linux Kernel 3.4 has been released few days ago. For new changes and prominent features in Linux 3.4, refer to this page.
This tutorial shows how to install the linux kernel 3.4.0 on Ubuntu 12.04 and 11.10. There’re two ways: installing the .deb packages and using the repositories of Ubuntu 12.10 (Quantal Quetzal).

NOTE: It’s not worth your while installing this new kernel unless old kernel has problems on your Ubuntu. Install the kernel at your own risk if you have decided to! It might break your system!

Method 1: It provides FTP downloading for .deb packages of Linux Kernel 3.4 (For Ubuntu 12.04 and 12.10). Ubuntu 12.04 go to this page and download following packages:

• for amd 64-bit:

  linux-headers-3.4.0-xxx-generic_3.4.0-xxx_amd64.deb
  linux-headers-3.4.0-xxx_3.4.0-xxx_all.deb
  linux-image-3.4.0-xxx-generic_3.4.0-xxx_amd64.deb

• for i386 32-bit:

  linux-headers-3.4.0-xxx-generic_3.4.0-xxx_i386.deb
  linux-headers-3.4.0-xxx_3.4.0-xxx_all.deb
  linux-image-3.4.0-xxx-generic_3.4.0-xxx_i386.deb

• i386 with more than 4GB RAM download pae kernel:

  linux-headers-3.4.0-xxx-generic-pae_3.4.0-xxx_i386.deb  
  linux-image-3.4.0-xxx-generic-pae_3.4.0-xxx_i386.deb

Method 2: Add repositories of Ubuntu 12.10 (Quantal Quetzal) by edit “/etc/apt/sources.list” and add following lines:

# Ubuntu Quantal Quetzal Repositories
deb http://security.ubuntu.com/ubuntu quantal-security main universe restricted multiverse
deb-src http://security.ubuntu.com/ubuntu quantal-security main universe restricted multiverse
deb http://it.archive.ubuntu.com/ubuntu/ quantal-updates main universe restricted multiverse
deb-src http://it.archive.ubuntu.com/ubuntu/ quantal-updates main universe restricted multiverse
deb http://it.archive.ubuntu.com/ubuntu/ quantal main universe restricted multiverse
deb-src http://it.archive.ubuntu.com/ubuntu/ quantal main universe restricted multiverse

Then update and install the kernel:

sudo apt-get update
sudo apt-get install linux

For PAE kernel:

sudo apt-get install linux-generic-pae

After installation, re-install device drivers of graphics card, sound card, wireless card, etc.

Finally, restart!