The style chosen will depend heavily on the style you're using for other elements of your document (for example fonts, page layout, sectional units formatting), so it's difficult to produce a "universal solution". Here's one possibility; I chose not to center it vertically but to use the double of space below the quote than the space above it; the width of the \parbox is calculated as the width of the longest line of the quote (stored in the length \longest):
\documentclass{article}
\usepackage{lmodern}
\newlength\longest
\begin{document}
\clearpage
\thispagestyle{empty}
\null\vfill
\settowidth\longest{\huge\itshape just as his inclination leads him;}
\centering
\parbox{\longest}{%
\raggedright{\huge\itshape%
A man ought to read \\
just as his inclination leads him; \\
for what he reads as a task \\
will do him little good.\par\bigskip
}
\raggedleft\Large\MakeUppercase{Samuel Johnson}\par%
}
\vfill\vfill
\clearpage
\end{document}

babrbara beeton suggested to place the author flush right as it's often used in epigraphs:
\documentclass{article}
\usepackage{lmodern}
\newlength\longest
\begin{document}
\clearpage
\thispagestyle{empty}
\null\vfill
\settowidth\longest{\huge\itshape just as his inclination leads him;}
\centering
\parbox{\longest}{%
\raggedright{\huge\itshape%
A man ought to read \\
just as his inclination leads him; \\
for what he reads as a task \\
will do him little good.\par\bigskip
}
\raggedleft\Large\MakeUppercase{Samuel Johnson}\par%
}
\vfill\vfill
\clearpage
\end{document}
\parbox; I've also added another options based on barbara beeton's comment. – Gonzalo Medina May 25 '12 at 13:33