You can do it the usual way:
\documentclass{article}
\usepackage[square,sort&compress,super]{natbib}
\usepackage{filecontents}
\begin{filecontents*}{mybib.bib}
@article{shell2002use,
title={{How to Use the IEEEtran \LaTeX{} Class}},
author={Shell, Michael},
journal={Journal of \LaTeX{} Class Files},
volume={1},
number={11},
pages={10--20},
year={2002}
}
\end{filecontents*}
\begin{document}
He said ``Bla blah''~\cite{shell2002use}
\bibliographystyle{unsrtnat}
\bibliography{mybib}
\end{document}

Or using the powerful csquotes
package. If you want links to be hyper links, add \usepackage{hyperref}
:
\documentclass{article}
\usepackage[square,sort&compress,super]{natbib}
\usepackage{filecontents}
\begin{filecontents*}{mybib.bib}
@article{shell2002use,
title={{How to Use the IEEEtran \LaTeX{} Class}},
author={Shell, Michael},
journal={Journal of \LaTeX{} Class Files},
volume={1},
number={11},
pages={10--20},
year={2002}
}
\end{filecontents*}
\usepackage{csquotes}
\usepackage[colorlinks]{hyperref}
\begin{document}
He said \enquote{Bla blah}~\cite{shell2002use}
\bibliographystyle{unsrtnat}
\bibliography{mybib}
\end{document}

Compile the above codes with pdflatex
→ bibtex
→ pdflatex
→ pdflatex
sequence.
natbib
is used mainly to get the citation numbers in super script notation.