When drawing FSM automata, tikz seems to eat the arrows

The tutorial does tikzset{->} globally. This is why it works in the tutorial. In my opinion this is a somewhat questionable approach.

documentclass{article}
usepackage{tikz}
usetikzlibrary{arrows,automata,positioning}
begin{document}
This is your code fragment:
begin{center}
begin{tikzpicture}
node[state, initial] (s1) {$s_1$};
node[state, right=2cm of s1] (s2) {$s_2$};
node[state, accepting, right=2cm of s2] (s3) {$s_3$};

draw   (s1) edge[loop above] node{0} (s1)
        (s1) edge[above] node{1} (s2)
        (s2) edge[loop above] node{1} (s2)
        (s2) edge[above] node{0} (s3);
end{tikzpicture}
end{center}

An appropriate way to get the arrow is to add texttt{->} in a emph{local
group}. (It gets added to the verb|draw| command.)
begin{center}
begin{tikzpicture}
node[state, initial] (s1) {$s_1$};
node[state, right=2cm of s1] (s2) {$s_2$};
node[state, accepting, right=2cm of s2] (s3) {$s_3$};

draw[->]   (s1) edge[loop above] node{0} (s1)
        (s1) edge[above] node{1} (s2)
        (s2) edge[loop above] node{1} (s2)
        (s2) edge[above] node{0} (s3);
end{tikzpicture}
end{center}

The tutorial you quote adds verb|tikzset{->}| emph{globally}.
tikzset{->}%
As you saw, this can lead to a lot of confusion, but it also adds the arrows.
begin{center}
begin{tikzpicture}
node[state, initial] (s1) {$s_1$};
node[state, right=2cm of s1] (s2) {$s_2$};
node[state, accepting, right=2cm of s2] (s3) {$s_3$};

draw   (s1) edge[loop above] node{0} (s1)
        (s1) edge[above] node{1} (s2)
        (s2) edge[loop above] node{1} (s2)
        (s2) edge[above] node{0} (s3);
end{tikzpicture}
end{center}

If I was you I would avoid adding this globally (and perhaps select another tutorial).

end{document}