You can use \nodes to place text everywhere you want. The are by default centered at the given coordinate which can be changed using the anchor and other options.
\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\draw[step=0.5cm,color=gray] (-1,-1) grid (1,1);
\node at (-0.75,+0.75) {A};
\node at (-0.25,+0.75) {B};
\node at (+0.25,+0.75) {C};
\node at (+0.75,+0.75) {D};
\node at (-0.75,+0.25) {E};
\node at (-0.25,+0.25) {F};
\node at (+0.25,+0.25) {G};
\node at (+0.75,+0.25) {H};
% ...
\node at (+0.75,-0.75) {Q};
\end{tikzpicture}
\end{document}

Or using a loop:
\documentclass{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\draw[step=0.5cm,color=gray] (-1,-1) grid (1,1);
\newcounter{mycount}
\setcounter{mycount}{`A}
\foreach \y in {+0.75,+0.25,-0.25,-0.75}
\foreach \x in {-0.75,-0.25,0.25,0.75}
\node at (\x,\y) {\char\value{mycount}\addtocounter{mycount}{1}};
\end{tikzpicture}%
% Or
\begin{tikzpicture}
\draw[step=0.5cm,color=gray] (-1,-1) grid (1,1);
\foreach \x/\y/\m in {+0.75/+0.75/A,-0.75/-0.75/X} % etc
\node at (\x,\y) {\m};
\end{tikzpicture}%
\end{document}

You can scale the image in the X or Y direction using xscale=<number> and yscale=<number>, respectively. Both are scaled with scale=<number>.
If you mean with "absolute position" a fixed position on a page you can do this by drawing it relative to the special current page node (needs the remember picture,overlay option on the picture). If you give more specific information about this I can make an example.
tabularwould not work? – Steven B. Segletes Jun 29 '15 at 16:23