[Tex/LaTex] How to draw a square and its diagonals with arrows

Question

I dno't know how to draw arrows as the above figure, and the code I wrote for the four points don't even show up on a result. Why my points don't appear? And what should be added for the arrows?

\documentclass{article}       
 \usepackage{tikz}     
 \begin{document}   
  \begin{tikzpicture}      
  \draw [fill=black](0, 0) circle;   
  \draw [fill=black](1, 0) circle;   
  \draw [fill=black](1, -1) circle;   
  \draw [fill=black](0, -1) circle;   
  \end{document}   

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\end{document}

Answer 1

\documentclass{article}       
\usepackage{tikz}     
\begin{document}   
\begin{tikzpicture}
\node[circle, draw=black, fill=black, name=0] at (0,0) {};
\node[xshift=-2mm] at (0.west) {0};

\node[circle, draw=black, fill=black, name=1] at (0,1) {};
\node[xshift=-2mm] at (1.west) {1};

\node[circle, draw=black, fill=black, name=3] at (1,0) {};
\node[xshift=2mm] at (3.east) {3};

\node[circle, minimum width=1pt, draw=black, fill=black, name=2] at (1,1) {};
\node[xshift=2mm] at (2.east) {2};


\draw[->, blue] (0) -- (2);
\draw[->, blue] (0) -- (3);
\draw[->, blue] (0) -- (1);
\draw[->, blue] (1) -- (2);
\draw[->, blue] (1) -- (3);
\draw[->, blue] (2) -- (3);

\end{tikzpicture}
\end{document}