if you're using the norm notation frequently, you might want to define a
command \norm using the \DeclarePairedDelimiter feature of mathtools:
\documentclass{article}
\usepackage{mathtools}
\DeclarePairedDelimiter\norm{\lVert}{\rVert}
\begin{document}
\[
\norm{a} + \norm[\bigg]{\frac{1}{a}}
\]
\end{document}

this "helper" command provides the ability to specify a size option as shown,
and a starred version automatically applies \left and \right.
mathtools automatically loads amsmath, loading that separately isn't necessary.
a more complete explanation of how to automatically provide \left and \right commands for paired delimiters is given by this question, and the present answer is a variant on the answer to that question by lev bishop.