In trying to adjust this answer in light of the OP's comments on another one, I discovered that I could not straightforwardly align an overlaid grid so that the steps began from the same point as the grid.
Why doesn't this work and how is this supposed to be done?
The code (minus my added bugs) is adapted from one of Michael Goerz's examples.
% Minor adaptions from http://michaelgoerz.net/notes/printable-paper-with-latex-and-tikz.html
\documentclass[a4paper, 10pt]{article} % for A4 size paper
\usepackage{tikz}
\begin{document}
\pagestyle{empty}
\colorlet{dlines}{green!25!black}
\colorlet{llines}{green!25!gray}
\tikzset{
dashed lines/.style={llines, very thin, densely dashed},
strong lines/.style={dlines, very thin},
}
\begin{tikzpicture}[remember picture, overlay]
\draw[style=dashed lines] (current page.south west) ++(5mm,8.5mm) coordinate (a) grid [step=10mm] ++(200mm,280mm) coordinate (b);
\draw[style=strong lines] (a) rectangle (b);
\draw[style=strong lines] (a) grid [step=20mm] (b);
\end{tikzpicture}
\end{document}