This guide is for almost every Linux distribution.

Prerequisite is that you have the required build tools installed already.
If not, do the following step:

Debian and Ubuntu users way;

sudo apt-get install build-essential

The Fedora/Red Hat way:

sudo yum groupinstall "Development Tools" "Legacy Software Development"

First step is getting the source package

wget http://ftp.gnu.org/gnu/bash/bash-4.0.tar.gz
Next step is compiling and installing it;

tar xf bash-4.0.tar.gz
./configure
make
sudo make install