How to compile the kernel in Linux?

First of all, download the kernel package you like from kernel.org or from the Ubuntu repositories.
If you want the official kernel patched by the Ubuntu Team, just type:
Code:

sudo apt-get install linux-tree

In this case we'll use the latest stable vanilla kernel version available.
For the compile process you'll need the following packages on Ubuntu:
Code:

sudo apt-get update
   sudo apt-get install build-essential
   sudo apt-get install kernel-package
   sudo apt-get install gcc
   sudo apt-get install libncurses5
   sudo apt-get install libncurses5-dev
   sudo apt-get install libqt3-mt-dev

Now untar the package:
Code:

cd /usr/src
   sudo tar --bzip2 -xvf linux-2.6.12.tar.bz2

Create the following symlink:
Code:

sudo ln -s /usr/src/linux-2.6.12 /usr/src/linux
   cd /usr/src/linux

Now you can start customizing your kernel configuration; there two way, the first one is graphical, the second one pseudo-graphical:
Code:

sudo make xconfig

Or:
Code:

sudo make menuconfig

Then, after having finished the customization, we have to start the compile process:
Code:

sudo make-kpkg clean
   sudo make-kpkg --append-to-version=-custom kernel_image modules_image

The revision flag is optional and is just useful to edit the kernel name showed through uname -r. You can write whatever you want instead of "-custom".

There's also another interesting and useful flag, that is --initrd. The vanilla kernel is not enable yet to make use of initrd properly, and in fact there's a patch for this. The Ubuntu official kernel is a vanilla kernel patched with some patches among which there's the one for initrd. So, if you are compiling a vanilla kernel, you should take --initrd out; otherwise, if you are compiling a Ubuntu kernel, you can make use of initrd and you probably would that.

Note that now you'll have a .deb package in /usr/src ready to be installed as any other package through a simple double-click.
Grub will be updated automatically.
So, just type:
Code:

sudo dpkg -i kernel-image-2.6.12-custom_10.00.Custom_i386.deb