Here's a pretty decent, but brief and high level, discussion of the structure of a water molecule. The first image gives a pretty good structural idea of what's going on, which is mostly that certain electron pairs are arranging themselves in a roughly tetrahedral pattern, two of the points of which correspond to the positions of the hydrogen atoms. It's more complex than that, of course (especially in liquid state, where the hydrogen atoms are actually breaking off and joining other molecules all the time), and some of the finer details are indeed measured rather than determined from first principles. However, the overall basic structure arises nicely from the electron interactions, so the fact that water makes nice hexagonal structures with open space when it freezes (responsible not only for the fact that ice floats, but also for all those pretty snowflakes) can be shown to arise simply from the fact that it's a molecule formed from an oxygen atom and two hydrogen atoms* and from the principles of quantum mechanics. Which is really pretty cool, if you think about it.

* And of course the fact that this combination forms a stable molecule at all is pretty easy to show from basic quantum physics, too!