Hey Diamond
I'm on the road (at
www.perimeterinstitute.ca - a very, very cool privately funded physics nerd kinda place where they have all sorts of whacky people) so sorry this wont be that comprehensive an answer - but I'll try and say something to stir Martin up and he can join in and do a better job (his field, not mine!)
The Einstein Equations are "derived" in as much as they follow naturally from the equivalence principle - Einsteins postulate that gravitational mass and inertial mass are equivalent - in fact exactly "the same". Its not completely clear to me how many hidden assumptions really go into the derivation - and so I've therefore never been sure that the equations are *necessary and sufficient*. Perhaps there are physical theories compatible with the EP that look completely different.
The equations dont mean much to look at unless you understand the whole machinary behind them. Basically they consist of equations containing parameters describing the curvature of spacetime on one side, being set equal to equations containing parameters that describe the stress-energy of matter+photon+... fields on the other side.
Its interesting that there is a sort of "logical fallacy" contained in GR that we never tell students about. In fact the only GR book I've seen discuss it at length is Rindler's. The "fallacy" is this: We would like to think of the field equations as truly fundamental. But ultimately they can only be considered consistency conditions. This is because we cannot describe the matter (plus other junk) fields (the one side of the equations) without making this description in spacetime - which amounts to an assumption about the background spacetime. However, the matter fields are meant to be directly dynamically interacting with and shaping the structure of this spacetime! What we do in practise is basically invoke symmetry principles that allow us to intuit what the structure of the spacetime must be like for special cases of matter fields, "put" the matter into this spacetime, and then check everything's consistent with the Einstein equations. Since we do all this under certain natural assumptions (weak fields, high symmetry etc) it doesnt keep the practioners awake at night, but for those who worry about the fundamentals of our physical theories this gives them headaches.
Methinks I'm not explaining it that well, but gotta go talk about the easy stuff over a few beers - like interpretations of Quantum Shmantum mechanics...
