Trouble inserting picture in CV template

No need for extra packages; simply include your image with a standard \includegraphics and use \smash, as in

The Netherlands\hfill 
\smash{\includegraphics[width=3cm]{example-image-a}}

A complete example:

The code:

\documentclass[10pt,a4paper]{article}
\usepackage[a4paper,margin=0.75in]{geometry}
\usepackage[english]{babel}
\usepackage{graphicx}
\usepackage{resume}

\begin{document}
\sloppy

\maintitle{Cies Breijs}{June 12, 1982}{}

\nobreakvspace{0.3em}

\noindent\href{mailto:cies.at.kde.dot.nl}{cies\mbox{}@\mbox{}kde.nl}\sbull
\textsmaller{+}31.646469087\sbull
{cies010} \emph{(Skype)}\sbull
\href{http://www.linkedin.com/in/ciesbreijs}{www.linkedin.com/in/ciesbreijs}
\\
Mathenesserplein 84\sbull
3022\thinspace {\large \sc ld}\sbull
Rotterdam\sbull
The Netherlands\hfill 
\smash{\includegraphics[width=3cm]{example-image-a}}

\spacedhrule{0.9em}{-0.4em}

\roottitle{Summary}

\end{document}

Update

If the image's height is too big, one could reduce it in \includegraphics, as in

\includegraphics[height=2cm]{example-image-a}

or use instead something like

The Netherlands\hfill 
\raisebox{-.5\totalheight}[0pt][.5\totalheight]{\includegraphics[width=3cm,height=5cm]{example-image-a}}

You can place the image explicitly. There are different possibilities to do this. In my opinion the easiest one is to use TikZ

Type \usepackage{tikz} inside your preamble to load the package. To include the image write below \begin{document}

\begin{tikzpicture}[remember picture, overlay]
  \node [anchor=north east, inner sep=0pt]  at (current page.north east)
     {\includegraphics[height=3cm]{example-image}};
\end{tikzpicture}

Another possibility is to use the textpos package.