Beamer text and image on the same slide

Use the columns environment to divide the slide into two columns. Then use \includegraphics to insert your image:

\documentclass{beamer}
\usetheme{Hannover}
\begin{document}
\begin{frame}
\frametitle{A frame}
  \begin{columns}[T]
    \begin{column}{.5\textwidth}
     \begin{block}{Your textblock}
% Your text here
    \end{block}
    \end{column}
    \begin{column}{.5\textwidth}
    \begin{block}{Your image}
% Your image included here
    \includegraphics[<options, e.g. width=\textwidth>]{<your image file>}
    \end{block}
    \end{column}
  \end{columns}
\end{frame}
\end{document} 

With minipage

You can also do this using a minipage:

Here's the corresponding LaTeX code where the image appears at the same time¹ as the third text item:

\documentclass{beamer}

% No "Figure:" prefix for image captions
\usepackage{caption}
\captionsetup[figure]{labelformat=empty}

% Define appearance of the slides
\usetheme{Rochester}
\usecolortheme{spruce}

\definecolor{ming}{HTML}{417E8C}

% Some themes don't include the slide number
\setbeamerfont{page number in head/foot}{size=\small}
\setbeamercolor{page number in head/foot}{fg=ming}
\setbeamertemplate{footline}[frame number]

\setbeamercolor{itemize item}{fg=ming}
\setbeamertemplate{itemize item}[circle]

% No navigation symbols at the slides' bottom
\beamertemplatenavigationsymbolsempty

% Insert a pause after every item.
% Show an item immediately by adding <.->
\beamerdefaultoverlayspecification{<+->}

\begin{document}
\frame{
  \frametitle{A test with images}
  \framesubtitle{The image appears with the third item}
  \begin{minipage}{0.5\textwidth}
    \begin{itemize}
      \item don't show the image yet
      \item wait for it...
      \item show the image now
      \item keep showing the image
      \item keep showing the image still
    \end{itemize}
  \end{minipage} \hfill
  \begin{minipage}{0.45\textwidth}
    % Show the image at item three and afterwards
    \uncover<3->{
      \begin{figure}
        % From https://i.imgur.com/AyzVOIO.jpg
        \includegraphics[height=0.9\textwidth]{asimo}
        \caption{here's the image!}
      \end{figure}
    }
  \end{minipage}
}
\end{document}

It's \uncover that allows to show elements when we reach a certain item in the presentation.

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¹ _{Synchronizing the appearance of the image with an item is something I couldn't figure out using columns.}