Translation (via Google translate):
Hello, I'm wanting to upgrade the kernel of my Linux version. I'm currently using 3.2.0-27-generic-pae and want to switch to the latest 3.4.7 from the official site.
More information on my computer:
Operating System: Ubuntu
Version: 12.04 (Precise) 32-bit
GNOME: 3.4.1
Memory: 1.8 GiB
Processor: Intel ® Pentium (R) Dual CPU [email protected] x 2
Here's a good start point: https://help.ubuntu.com/community/Kernel/Compile/
You may use many other sources on Linux kernel 3.2 (like http://mitchtech.net/compile-linux-kernel-on-ubuntu-12-04-lts-detailed/) as it's almost the same for Linux kernel 3.4.
Then, if you face any problem, you can search for a solution or come back here and ask about it.
There is no official version of kernel 3.4.7 for Ubuntu. The Ubuntu kernel team produces unofficial "mainline" builds for testing purposes only, but for kernels 3.4+, they are doing it for Ubuntu 12.10 (quantal) only.
You can get the 3.4.7 mainline kernel from http://kernel.ubuntu.com/~kernel-ppa/mainline/v3.4.7-quantal/.
Install both the generic and the extra packages for your i386 architecture: