1

I want to have this result: The first column in grey and the second color is white:

Two columns page with two colors

I am using \usepackage{multicol}.

2

your question isn't so vivid, but I prefer tikz and atbegshi.

\documentclass{article}

\usepackage{tikz}
\usepackage{atbegshi}
 \usepackage{lipsum}
 \usepackage{multicol}

 \AtBeginShipout{\AtBeginShipoutAddToBox{%
 \begin{tikzpicture}[remember picture, overlay]
    \draw [fill=gray, opacity=.3] (\marginparwidth-\marginparsep, -\headheight-\headsep) rectangle 
    (\marginparwidth+\columnwidth,-\textheight-\headheight-2\headsep); 
 \end{tikzpicture}%
 }}
 \begin{document}
\begin{multicols}{2}
 \lipsum[1-40]
 \end{multicols}
 \end{document}

enter image description here

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