By default TeX prints the page number at the bottom of the page. I added a custom header so that the page number appears in the top right hand corner.

So I have the page number in two places, at the bottom of the page and in my header.

How do I get rid of the page number that is at the bottom of the page?

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This depends on how you place the page number in the top right. Is it done using fancyhdr? Then you can add \fancyhf{} at the start of your fancy page style definition to clear everything before setting only the header. – Werner Dec 20 '12 at 20:09
Note that the default for chapter-style pages (in the supported document classes, like report and book) set the first page of each chapter as plain. So which \documentclass are you using? – Werner Dec 20 '12 at 20:11

I would suggest using the fancyhdr package. It allows you to set the headers and footers.

\documentclass{article}
\usepackage{lipsum}
\usepackage{fancyhdr}
\pagestyle{fancy}
%%
\lfoot{Left footer}
\cfoot{Center of footer}
\rfoot{Right of footer}
%%