To make the axis lines go through the origin, set axis lines=middle. To get a grid, set grid=both.
\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
axis lines=middle, % Axis lines go through the origin
grid=both, % Activate grid for both dimensions
after end axis/.code={ % To get labels for the origin
\path (axis cs:0,0)
node [anchor=north west,yshift=-0.075cm] {0}
node [anchor=south east,xshift=-0.075cm] {0};
}
]
\addplot [
only marks, % So there are no connecting lines between the points
error bars/x dir=both, error bars/y dir=both, % Activate error bars in both dimensions
error bars/x explicit, error bars/y explicit, % Error values will be provided for each coordinate
] table [
x error=error_x, % Columns to use for the error values
y error=error_y
]{
x y error_x error_y
1 2.1 0.3 0.4
-2.5 -1.3 0.5 0.2
5 -1.9 0.8 1.1
};
\end{axis}
\end{tikzpicture}
\end{document}

xmin=<...>, xmax=<...>, ymin=<...>, ymax=<...>(but that's really something you could have looked up in the manual). – Jake Sep 12 '14 at 07:33