When you install git on your computer, you may find new variables available in the environment, it is $(__git_ps1). This variable contains the branch name of the current repository. The only thing you need to edit ~/.bashrc and add $(__git_ps1) to the PS1 definition in this way

if [ "$color_prompt" = yes ]; then
    PS1='${debian_chroot:+($debian_chroot)}\[\033[01;32m\]\u@\h\[\033[00m\]:\[\033[01;34m\]\w\[\033[00m\]$(__git_ps1)\$ '
else
    PS1='${debian_chroot:+($debian_chroot)}\u@\h:\w$(__git_ps1)\$ '
fi

N.B. the $(__git_ps1) is available by default for Ubuntu >= 14.04, you may check if it works by just going to any git repository and run echo $(__git_ps1)

~/Work/moiseevigor.github.io $ echo $(__git_ps1);
(master)

If you see an empty string, so just source it from /etc/bash_completion.d/git, and in this case the ~/.bashrc will look like

source /etc/bash_completion.d/git

if [ "$color_prompt" = yes ]; then
    PS1='${debian_chroot:+($debian_chroot)}\[\033[01;32m\]\u@\h\[\033[00m\]:\[\033[01;34m\]\w\[\033[00m\]$(__git_ps1)\$ '
else
    PS1='${debian_chroot:+($debian_chroot)}\u@\h:\w$(__git_ps1)\$ '
fi

This is it, now you have a gorgeous prompt

:~/moiseevigor.github.io (master)$ 

Have a nice branching!