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-4.1.tar.gz
Next step is compiling and installing it;
tar xf bash-4.1.tar.gz
cd bash-4.1*
./configure
make
sudo make install