I absolutely agree with Alan Munn with one limitation: His answer might give the impression that the fancyhdr package is without alternative. However, there are some other packages to configure the page header and page footer.
Here I've adapted his example for using package scrlayer-scrpage instead of fancyhdr:
\documentclass{article}
\usepackage{scrlayer-scrpage}
\usepackage{lipsum} % only for showing some sample text
\clearpairofpagestyles% remove all default elements from page styles scrheadings
% and plain.scrheadings
\ofoot*{\pagemark}% add pagination to the outer part of the page footer
\begin{document}
\lipsum
\end{document}

Using scrlayer-scrpage would also be recommended using a KOMA-Script class like scrartcl instead of a standard class:
\documentclass{scrartcl}
\usepackage{scrlayer-scrpage}
\usepackage{lipsum} % only for showing some sample text
\cfoot*{}% remove the default center pagination from the footer
\ofoot*{\pagemark}% add pagination to the outer part of the page footer
\begin{document}
\lipsum
\end{document}
I've used here another solution to remove the default pagination in the middle of the footer. You can find more examples for using scrlayer-scrpage in the manual and in the KOMA-Script wiki (also available in German).
For such a simple page style with pagination only, you could also use package scrlayer:
\documentclass{article}
\usepackage{scrlayer}
\usepackage{lipsum} % only for showing some sample text
\DeclareNewLayer[% declare a new layer
foreground,% printed in the foreground
foot,% placed to the page footer
contents={\hfill\thepage}% with right aligned page number as content
]{pagenumber}
\RedeclarePageStyleByLayers{plain}{pagenumber}% redefine page style plain to use the newly defined layer
\pagestyle{plain}% (re)activate the (re)defined page style
\begin{document}
\lipsum
\end{document}
As you can see, package scrlayer is more low-level than scrlayer-scrpage. Package scrlayer-scrpage adds an extra user level to package scrlayer.
Here I've adapted his example for using package titleps instead of fancyhdr:
\documentclass{article}
\usepackage{titleps}
\usepackage{lipsum} % only for showing some sample text
\newpagestyle{pagenumberfooterright}{% defining a new page style
\setfoot{}{}{\thepage}% with page number at the right side
}
\pagestyle{pagenumberfooterright}
\begin{document}
\lipsum
\end{document}

See the manuals of the packages for more information.
fancyhdrdidn't change any margin ... However, what documentclass you are using? – Jan 12 '11 at 21:08