The “related” and in the comments linked question deal, sadly, only with content that is not on one path.
The manual solution
Creating two paths, where the second (longer one) is only uncovered in the second slide.
\visible<1>{\draw(0,0)--(1,0);}
\visible<2->{\draw(0,0)--(1,0)--(1,1);}
We could use the first \draw without \visible as it just gets over-drawn, but maybe you want to play around with opacity or hide stuff again.
The better (?) solution
Changing the line to in the first slide to move to (better would be just leave me alone but use the correct bounding box so that the picture doesn't jump around but in this case it works just fine)†.
In this particular minimal example, beamer doesn't know that there's a second slide when we use only onslide=<1>, so we need to clarify that.
Variant A
Specifying the second (and following) operation as line to or empty as the default to path is line to (a.k.a. --).
Variant B
Creating a second slide somehow (\only<2>{}), again using the fact that the default to is a line to operation.
Better-er
Creating a TikZ style that combines hiding and showing.
hideshow/.style args={<#1><#2>#3}{%
onslide=<#1>{move to},
onslide=<#2>{#3}
}
Code
\documentclass{beamer}
\usepackage{tikz}
\tikzset{
onslide/.code args={<#1>#2}{% http://tex.stackexchange.com/a/6155/16595
\only<#1>{\pgfkeysalso{#2}}
},
hideshow/.style args={<#1><#2>#3}{%
onslide=<#1>{move to},
onslide=<#2>{#3}
}
}
\begin{document}
\begin{frame}% manual
\begin{tikzpicture}[scale=5,very thick]
\visible<1>{\draw(0,0)--(1,0);}
\visible<2->{\draw(0,0)--(1,0)--(1,1);}
\end{tikzpicture}
\end{frame}
\begin{frame}% "better" A
\begin{tikzpicture}[scale=5,very thick]
\draw(0,0)--(1,0) to[onslide=<1>{move to},onslide=<2>{}] (1,1);% or onslide=<2>{line to}
\end{tikzpicture}
\end{frame}
\begin{frame}\only<2>{}% "better" B
\begin{tikzpicture}[scale=5,very thick]
\draw(0,0)--(1,0) to[onslide=<1>{move to}] (1,1);
\end{tikzpicture}
\end{frame}
\begin{frame}% "better-er"
\begin{tikzpicture}[scale=5,very thick]
\draw(0,0)--(1,0) to[hideshow=<1><2>{}] (1,1);
\end{tikzpicture}
\end{frame}
\end{document}
Output (cropped)

† Apparently such key is not needed, see the output of the following code:
\documentclass[beamer]{standalone}
\usepackage{tikz}
\tikzset{
onslide/.code args={<#1>#2}{
\only<#1>{\pgfkeysalso{#2}}
},
hideshow/.style args={<#1><#2>#3}{%
onslide=<#1>{move to},
onslide=<#2>{#3}
}
}
\begin{document}
\begin{frame}
\begin{tikzpicture}[scale=5,very thick]
\draw[line width=1cm,line join=round](0,0)--(1,0) to[hideshow=<1><2->{}] (1,1);
\end{tikzpicture}
\end{frame}
\end{document}
TikZcommands (i.e. they are about overlays between\sometikzcommand1[options] <overlay_part_1>;and\sometikzcommand2[options] <overlay_part_2>;). In my problem, however, I need overlay within ONETikZcommand, i.e.\tikzcommand[options] <overlay_part_1> ... <overlay_part_2>. I'm not sure I see how to apply the methods suggested in those two posts... – Herr K. Nov 20 '12 at 05:46