Braket notation in LaTeX

There is the physics package:

\documentclass{article}
\usepackage{physics}
\begin{document}
  $\bra{\Psi}\ket{\Psi}$ $\expval{A}{\Psi}$
\end{document}

It offers many other goodies for typsetting physics things. Details can be found in the manul (texdoc physics from command prompt/terminal).

Use \braket{0|0}:

\documentclass{standalone}

\usepackage{braket}

\begin{document}

$\braket{0|0}$

\end{document}

A solution using the mathtools package:

\documentclass{article}

\usepackage{mathtools}
\DeclarePairedDelimiter\bra{\langle}{\rvert}
\DeclarePairedDelimiter\ket{\lvert}{\rangle}
\DeclarePairedDelimiterX\braket[2]{\langle}{\rangle}{#1 \delimsize\vert #2}

\begin{document}

\begin{align*}
  \bra{a}       &= \bra*{\frac{a}{1}} \\
  \ket{a}       &= \ket*{\frac{a}{1}} \\
  \braket{a}{b} &= \braket*{\frac{a}{1}}{\frac{b}{1}}
\end{align*}

\end{document}

Notice that the starred versions of the macros scale automatically.