This is quite easy: just use \node[right] to tell TikZ to fraw the nodes rightward from the specified position:
\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{figure}
\begin{tikzpicture}
\node[right] at (1.0, 2.0) {veeeeeeeeeeery long text node};
\node[right] at (1.0, 1.0) {short text node};
\end{tikzpicture}
\end{figure}
\end{document}

If you want the texts not that far apart, you can do it without trying by using named nodes for referencing:
\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{figure}
\begin{tikzpicture}
\node[right,inner sep=0,minimum height=0.6cm] (a) at (1.0, 2.0) {veeeeeeeeeeery long text node};
\node[below right,inner sep=0,minimum height=0.6cm] (b) at (a.south west) {short text node};
\node[below right,inner sep=0,minimum height=0.6cm] (c) at (b.south west) {another text node};
\node[below right,inner sep=0,minimum height=0.6cm] (d) at (c.south west) {yet another text node};
\end{tikzpicture}
\end{figure}
\end{document}

If you use the align=<key> option for the node, you can also use \\ inside the node for line breaking, thus putting all the content in a single node:
\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{figure}
\begin{tikzpicture}
\node[align=left] {veeeeeeeeeeery long text node\\ short text node\\ another text node\\yet another text node};
\end{tikzpicture}
\end{figure}
\end{document}

If it does not matter where the line breaks occur, you can use the text width=<length> option to automatically break the text:
\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{figure}
\begin{tikzpicture}
\node[text width=5cm] {veeeeeeeeeeery long text node; short text node; another text node; yet another text node};
\end{tikzpicture}
\end{figure}
\end{document}
