I think the syntax might be straight forward, but the layout of your columns should highly depend on what your trying to explain/show/tell. Just straight taking your tabular and putting it into LaTeX using booktabs for style and floatrow to center the tabular and putting the caption above using the code
\documentclass[a4paper,12pt]{scrartcl}
\usepackage[utf8]{inputenc}
\usepackage{booktabs,floatrow}
%center tables
\floatsetup[table]{objectset=centering,capposition=top}
\begin{document}
For a straight forward thingy see Table~\ref{Tab1}.
\begin{table}
\begin{tabular}{lllll}\toprule
&&\textbf{Backward} & \textbf{Forward} & \textbf{Bidirectional}\\\midrule
atis & Training & 345 & 235 & 345\\
& Test & 356 & 252 & 345\\
brown & Training & 465 & 345 & 346\\
& Test & 456 & 342 & 253\\
wsj & Training & 345 & 235 & 254\\
& Test & 4336 & 634 & 3434
\\\bottomrule
\end{tabular}
\caption{The Results}\label{Tab1}
\end{table}
\end{document}
results in the tabular as seen here

But to me it looks like you want to compare Training and Test for certain methods, each applied to one „Object of interes“ (artis, brown & wsj) - so maybe you want to spend one column for each object and get a better way to compare those two by using something like „subcolumns“ as in the following MWE
\documentclass[a4paper,12pt]{scrartcl}
\usepackage[utf8]{inputenc}
\usepackage{booktabs,floatrow}
%center tables
\floatsetup[table]{objectset=centering,capposition=top}
\begin{document}
But maybe also the Table~\ref{Tab2} might be nice?
\begin{table}
\begin{tabular}{lrrrrrr}\toprule
&\multicolumn{2}{c}{\textbf{Backward}}&\multicolumn{2}{c}{\textbf{Forward}}&\multicolumn{2}{c}{\textbf{Bidirectional}}
\\\cmidrule(r){2-3}\cmidrule(r){4-5}\cmidrule(r){6-7}
&Training&Test&Training&Test&Training&Test\\\midrule
atis & 345 & 356
& 235 & 252
& 345 & 345\\
brown & 465& 456
& 345 & 342
& 346 & 253\\
wsj & 345 & 4336
& 235 & 634
& 254 & 3434
\\\bottomrule
\end{tabular}
\caption{The Results}\label{Tab2}
\end{table}
\end{document}
Where i used \cmidrow additionally to group each of the Training-Test-Pairs and used \multicolumn to give these two columns a common title. The result is

But that of course depends on your data, I assumed here, that Training and Test belonged to the same object, (atis for example) hence putting them in one row seems to be a good idea.
Edit: For the first idea i just used l as left for the column layout, the second one is the one i prefer (r for right), but of course egreg's answer using siunitx is quite nice, too.
booktabspackage. – Peter Grill Feb 15 at 5:27