Very few of the fonts available for pdflatex have a precomposed ‘ǚ’ character, but it can be built from other pieces. However, TeX doesn't allow to pile up accents in a straightforward way, so it's better to put one accent over a precomposed ’ü’, which can be done with T1 encoded fonts. Therefore you can get the character with \v{\"u} if you say
\usepackage[T1]{fontenc}
in the preamble. You can also use the character directly for input with
\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{newunicodechar}
\newunicodechar{ǚ}{\v{ü}}
\begin{document}
Typesetting the `ǚ' character
\end{document}
that renders as

If you're willing to use the Libertine fonts, as suggested by Leo Liu, the definition is slightly different
\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{newunicodechar}
\newunicodechar{ǚ}{\libertineGlyph{uni01DA}}
\begin{document}
Typesetting the `ǚ' character
\end{document}

A different strategy is to switch to XeLaTeX or LuaLaTeX:
\documentclass{article}
\usepackage{fontspec}
% omitting the following line would use the Latin Modern fonts
\setmainfont[Ligatures=TeX]{Linux Libertine O}
\begin{document}
Typesetting the `ǚ' character
\end{document}

ǚdirectly with XeTeX. – Leo Liu May 23 '12 at 06:41\usepackage[T1]{fontenc}, then\v{\"{u}}works. – egreg May 23 '12 at 06:49\usepackage{lmodern}. – matth May 23 '12 at 07:16