Fancy Equations in Latex/beamer with Tikz

LaTeXSo, when I discovered that Tikz and Beamer are made by one and the same guy (Till Tantau), I was very much pleased, since I then assumed that I could use the \onslide<> command inside tikzpictures (to make fancy equations, as hinted at in the title). It turns out that this is indeed the case, though complications arose in connections to this, and I thought I would document here how I went about it:
So, the mission was simple: use Tikz to make equations with colored labels on the terms.