The interactive examples in this post require installing Wolfram CDF player, which is free and works on most desktop computers using Firefox, Safari and Internet Explorer, but not Chrome. The source code is the Mathematica Notebook Live evaluation of expressions in TreeForm 3, which is available for free use under a Creative Commons Attribution-ShareAlike 2.5 License. The code is ad-hoc. It might be worthwhile for someone to design a package that produces this sort of tree for any expression. The notebook can be read by CDF Player if you cannot make the embedded versions in this post work.
This demonstration shows the step by step computation of the value of the expression $3x^2+2(1+y)$ shown as a tree. By moving the first slider from right to left, you go through the six steps of the computation. You may select the values of $x$ and $y$ with the second and third sliders. If you click on the plus sign next to a slide, a menu opens up that allows you to make the slider move automatically, shows the values, and other things.
Note that subtrees on the same level are evaluate left to right. Parallel processing would save two steps.
A previous post related to this post is Making visible the abstraction in algebraic notation.