Your rectangle is a node. Hence you can place an arrow shaped node at its anchors like south and east.
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{shapes.arrows}
\tikzset{
myarrow/.style={
draw,thick,
single arrow,
text width=1cm,
fill=white
},
}
\begin{document}
\begin{tikzpicture}
\node [draw,rectangle,minimum size=4cm](r){};
\node[myarrow,rotate=90] at (r.east){};
\node[myarrow] at (r.south){};
\end{tikzpicture}%
\end{document}

For modifying the shape of the arrow, you may refer to pgfmanual page 725, section 67.5, under shape single arrow.
\documentclass...\begin{document}...\end{document}, it should compile and contain close to the minimal amount of code needed to explain/demonstrate what you are asking. This saves everyone time:) – Apr 21 '15 at 13:56