There are many ways, and it all depends on the desired final layout. Below, two options: one using the standard quote environment; the other one using mdframed:
\documentclass{article}
\usepackage[framemethod=tikz]{mdframed}
\usepackage{lipsum}
\newmdenv[linecolor=cyan,backgroundcolor=cyan!20]{question}
\begin{document}
\lipsum[2]
\begin{quote}
\lipsum[2]
\end{quote}
\lipsum[2]
\begin{question}
\lipsum[2]
\end{question}
\lipsum[2]
\end{document}

And with tcolorbox:
\documentclass{article}
\usepackage{tcolorbox}
\tcbuselibrary{most}
\usepackage{lipsum}
\newtcolorbox{question}{breakable,colframe=cyan,colback=cyan!20}
\begin{document}
\lipsum[2]
\begin{question}
\lipsum[2]
\end{question}
\lipsum[2]
\end{document}

Another option using a list through changepage:
\documentclass{article}
\usepackage{changepage}
\usepackage{lipsum}
\newenvironment{question}
{\par\smallskip\begin{adjustwidth}{1em}{1em}\small\itshape}
{\end{adjustwidth}\par\smallskip}
\begin{document}
\lipsum[2]
\begin{question}
\lipsum[2]
\end{question}
\lipsum[2]
\end{document}

The options using mdframed and tcolorbox offer you many customization possibilities; please refer to the documentation of the packages.
For example, you can define your structure as a theorem-like block using, for example, amsthm and then surround it with a mdframed:
\documentclass{article}
\usepackage[framemethod=tikz]{mdframed}
\usepackage{amsthm}
\usepackage{lipsum}
\newtheorem{question}{Question}
\mdfdefinestyle{que}{
linecolor=cyan,
backgroundcolor=cyan!20,
}
\surroundwithmdframed[style=que]{question}
\begin{document}
\lipsum[2]
\begin{question}
\lipsum[2]
\end{question}
\lipsum[2]
\end{document}

A numbered structure with tcolorbox:
\documentclass{article}
\usepackage{tcolorbox}
\usepackage{lipsum}
\newtcolorbox[auto counter]
{question}
{colback=cyan!20,colframe=cyan,fonttitle=\bfseries,
title=Question~\thetcbcounter}
\begin{document}
\lipsum[2]
\begin{question}
\lipsum[2]
\end{question}
\lipsum[2]
\end{document}
