How do I write the norm of a vector?

You can simply use

||x||

in math mode to have the norm of x.

You may want to define a new command that wraps the functionality by putting

\newcommand{\vectornorm}[1]{\left|\left|#1\right|\right|}

in the preamble of your document and then use it as

\vectornorm{x}.

The occurrences of \left and \right in the command allow the pipe symbols (|) to grow with the size of the symbol that is within the norm.