I get 1.0 Nm. But how to get 1.0 N.m
\documentclass{article}
\usepackage{siunitx}
\begin{document}
\SI{1.0}{\newton\meter}\\
1.0~N$\cdot$m
\end{document}

I get 1.0 Nm. But how to get 1.0 N.m
\documentclass{article}
\usepackage{siunitx}
\begin{document}
\SI{1.0}{\newton\meter}\\
1.0~N$\cdot$m
\end{document}

inter-unit-product is an available option and described in the documentation. To get correct spacing you should use ${}\cdot{}$. However I prefer a tighter spacing by $\cdot$.
\documentclass{article}
\usepackage{siunitx}
\parindent0pt
\begin{document}
\SI[inter-unit-product =$\cdot$]{1.0}{\newton\meter}\\
\SI[inter-unit-product =${}\cdot{}$]{1.0}{\newton\meter}\\
$1.0\,\mathrm{N}\cdot\mathrm{m}$
\end{document}

To set his behavior for the whole document you can specify the option via \sisetup
\sisetup{inter-unit-product =$\cdot$}
Sorry for the zombie reply, but aren't the units typeset in math mode? In that case:
\SI[inter-unit-product =$\cdot$]{1.0}{\newton\meter}
won't compile. You should use:
\SI[inter-unit-product =\ensuremath{\cdot}]{1.0}{\newton\meter}
instead.
\SI command has changed to \qty command. And you can still use the old commands, the author says "Where possible, older names are mapped to newer ones internally: you will be warned in the log if this is the case."
– Gordon Bai
Jul 05 '21 at 15:00
\sisetup{inter-unit-product =$\cdot$}– Marco Daniel Jun 08 '12 at 08:54\si[inter-unit-product = \ensuremath{{}\cdot{}}]to get the corrected spacing. – Svend Tveskæg Apr 10 '13 at 12:57$-symbols:\usepackage[inter-unit-product =\cdot]{siunitx}– Steeven May 11 '17 at 07:15\cdotis a math operator; therefore, I would say that it should be treated as such, i.e., the\cdothas to be in mathmode. – Svend Tveskæg Nov 06 '20 at 16:29