The Dreden theme uses as outer theme miniframes specifying that the footline is of type authorinstitutetitle
\useoutertheme[footline=authorinstitutetitle]{miniframes}
Thus, to insert the frame number (command \insertframenumber) with respect to the total frame number (command \inserttotalframenumber) we should take into account how the authorinstitutetitle is defined:
\def\beamer@theme@footline@authorinstitutetitle{
\defbeamertemplate*{footline}{miniframes theme}
{%
\begin{beamercolorbox}[colsep=1.5pt]{upper separation line foot}
\end{beamercolorbox}
\begin{beamercolorbox}[ht=2.5ex,dp=1.125ex,%
leftskip=.3cm,rightskip=.3cm plus1fil]{author in head/foot}%
\leavevmode{\usebeamerfont{author in head/foot}\insertshortauthor}%
\hfill%
{\usebeamerfont{institute in head/foot}\usebeamercolor[fg]{institute in head/foot}\insertshortinstitute}%
\end{beamercolorbox}%
\begin{beamercolorbox}[ht=2.5ex,dp=1.125ex,%
leftskip=.3cm,rightskip=.3cm plus1fil]{title in head/foot}%
{\usebeamerfont{title in head/foot}\insertshorttitle}%
\end{beamercolorbox}%
\begin{beamercolorbox}[colsep=1.5pt]{lower separation line foot}
\end{beamercolorbox}
}
}
Now, in the lower right corner there's nothing thus it is possible to exploit the space in:
\begin{beamercolorbox}[ht=2.5ex,dp=1.125ex,%
leftskip=.3cm,rightskip=.3cm plus1fil]{title in head/foot}%
{\usebeamerfont{title in head/foot}\insertshorttitle}%
\end{beamercolorbox}%
by adding:
\begin{beamercolorbox}[ht=2.5ex,dp=1.125ex,%
leftskip=.3cm,rightskip=.3cm plus1fil]{title in head/foot}%
{\usebeamerfont{title in head/foot}\insertshorttitle}%
\hfill%
{\usebeamerfont{frame number}\usebeamercolor[fg]{frame number}\insertframenumber~\frameofframes~\inserttotalframenumber}
Notice that as separator between the frame numbers there's a command: \frameofframes. It is defined as:
\newcommand{\frameofframes}{/}
\newcommand{\setframeofframes}[1]{\renewcommand{\frameofframes}{#1}}
This allows you to modify the standard representation (1/5 for example), with something else; for instance:
\setframeofframes{of}
will provide 1 of 5.
The code:
\documentclass{beamer}
\usepackage{lmodern}
\usetheme{Dresden}
\author{My name}
\title{My presentation}
\institute{My institute}
\newcommand{\frameofframes}{/}
\newcommand{\setframeofframes}[1]{\renewcommand{\frameofframes}{#1}}
\setframeofframes{of}
\makeatletter
\setbeamertemplate{footline}
{%
\begin{beamercolorbox}[colsep=1.5pt]{upper separation line foot}
\end{beamercolorbox}
\begin{beamercolorbox}[ht=2.5ex,dp=1.125ex,%
leftskip=.3cm,rightskip=.3cm plus1fil]{author in head/foot}%
\leavevmode{\usebeamerfont{author in head/foot}\insertshortauthor}%
\hfill%
{\usebeamerfont{institute in head/foot}\usebeamercolor[fg]{institute in head/foot}\insertshortinstitute}%
\end{beamercolorbox}%
\begin{beamercolorbox}[ht=2.5ex,dp=1.125ex,%
leftskip=.3cm,rightskip=.3cm plus1fil]{title in head/foot}%
{\usebeamerfont{title in head/foot}\insertshorttitle}%
\hfill%
{\usebeamerfont{frame number}\usebeamercolor[fg]{frame number}\insertframenumber~\frameofframes~\inserttotalframenumber}
\end{beamercolorbox}%
\begin{beamercolorbox}[colsep=1.5pt]{lower separation line foot}
\end{beamercolorbox}
}
\makeatother
\begin{document}
\section{One}
\subsection{One-one}
\frame{\frametitle{X-one} bla bla bla}
\frame{\frametitle{X-one-a} bla bla bla}
\frame{\frametitle{X-one-b} bla bla bla}
\subsection{One-two}
\frame{\frametitle{X-one} bla bla bla}
\frame{\frametitle{X-one-a} bla bla bla}
\frame{\frametitle{X-one-b} bla bla bla}
\section{Two}
\subsection{Two-one}
\frame{\frametitle{X-one} bla bla bla}
\frame{\frametitle{X-one-a} bla bla bla}
\frame{\frametitle{X-one-b} bla bla bla}
\subsection{Two-two}
\frame{\frametitle{X-one} bla bla bla}
\frame{\frametitle{X-one-a} bla bla bla}
\frame{\frametitle{X-one-b} bla bla bla}
\section{Three}
\subsection{Three-one}
\frame{\frametitle{X-one} bla bla bla}
\frame{\frametitle{X-one-a} bla bla bla}
\frame{\frametitle{X-one-b} bla bla bla}
\subsection{Three-two}
\frame{\frametitle{X-one} bla bla bla}
\frame{\frametitle{X-one-a} bla bla bla}
\frame{\frametitle{X-one-b} bla bla bla}
\end{document}
One frame as result:
You do need to tell beamer what you want to appear in each frame of the handout version. You can use \onslide specifications to do this so that you do not need to modify the existing overlay specifications at all. (I'm not sure this is what you want - probably not.)
The following code modifies your MWE so that, in presentation mode, there would actually be 10 slides within the frame. These are then placed on slides 1 or 2 of the handout. This is a waste of code: if you only want to show slide 5 and slide 10, you do not need two \againframe but only one. But, anyway, with the two:
\documentclass[handout]{beamer}
\begin{document}
\begin{frame}<1-| handout:0>[label=foo]{My only frame}
\begin{enumerate}[<+->]% or whatever you like for presentation mode
\onslide<1-| handout:1-2>
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\onslide<1-| handout:2>
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\end{enumerate}
\end{frame}
\againframe<0| handout:1>{foo}
\againframe<0| handout:2>{foo}
\end{document}
More efficiently with only one repeat:
\documentclass[handout]{beamer}
\begin{document}
\begin{frame}<1-| handout:1>[label=foo]{My only frame}
\begin{enumerate}[<+->]% or whatever you like for presentation mode
\onslide<1-| handout:1-2>
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\onslide<1-| handout:2>
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\end{enumerate}
\end{frame}
\againframe<0| handout:2>{foo}
\end{document}
I'm not sure how this could apply to article mode since then there are no frames or slides.
Best Answer
Following code shortens navigation line and includes page number on left side. Is this what you want?