I need to arrange three figures in a two column document as follows

Comments
You did not tell us about the individual/main captions and/or references. I decided to throw that in as well.
Basic Idea
For a two column document use the option [twocolumn] with the \documentclass.
Create a two column table (outer table). Put another single column table in the first column. Put the first two images (A and B) as the two rows of the inner table. Put the third image (B) in the second column of the outer table.
Use subcaption to take care of captions and labels. (This answer helps.)
The Solution
\documentclass[twocolumn]{article}
\usepackage{graphicx}
\usepackage{caption}
\usepackage{subcaption}
\usepackage{lipsum} % For dummy text only
\begin{document}
\begin{figure}[!t]
\begin{tabular}[b]{cc}
\begin{tabular}[b]{c}
\begin{subfigure}[b]{0.4\columnwidth}
\includegraphics[width=\textwidth]{A.png}
\caption{A.}
\label{fig:A}
\end{subfigure}\\
\begin{subfigure}[b]{0.4\columnwidth}
\includegraphics[width=\textwidth]{B.png}
\caption{B.}
\label{fig:B}
\end{subfigure}
\end{tabular}
&
\begin{subfigure}[b]{0.4\columnwidth}
\includegraphics[width=\textwidth]{C.png}
\caption{C.}
\label{fig:C}
\end{subfigure}
\end{tabular}
\label{fig:ABC}
\caption{A, B and C.}
\end{figure}
\lipsum[1-5]
\end{document}
The Output

Further Tweaking
Change the 0.4\columnwidths to tweak image sizes. Watch for overfull boxes.
Your question seems to involve two different parts:
The answer to 1. is to use the twocolumn option in the article class.
The answer to 2. is to use a minipage environment.
\documentclass[twocolumn]{article}
\usepackage{graphicx}
\usepackage{lipsum}
\begin{document}
\begin{figure}[h!]
\begin{minipage}{0.48\columnwidth}
\includegraphics[width=\columnwidth,height=4cm]{triangle}
\\[3mm]
\includegraphics[width=\columnwidth,height=4cm]{triangle}
\end{minipage}
\begin{minipage}{0.48\columnwidth}
\includegraphics[width=\columnwidth,height=83mm]{triangle}
\end{minipage}
\end{figure}
\lipsum[1-7]
\end{document}

The code to generate the triangle.pdf file is
\documentclass{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\draw[fill=green!20] (0,0) -- (1,1) -- (1,0) -- cycle;
\end{tikzpicture}
\end{document}
example-image-a which comes bundled with mwe package. There is also -b and -c in addition to -a above. Further, there is no need of loading mwe if you just want to use these images like \includegraphics{example-image-b}. :-)
–
Dec 31 '13 at 22:58