We can't understand how quantum mechanics and the general theory of relativity could reconcile without first understanding how they -- right now -- do not. Because it turns out that neither one really works if the other is true.
Einstein said that space-time is a smooth constant, and that only big things can warp it. Quantum mechanics said that the smallest parts of the universe are constantly, dramatically fluctuating and changing.
If quantum mechanics is correct and everything is in fuzzy motion constantly, then gravity wouldn't work the way Einstein predicted. Space-time would also have to be constantly at odds with everything around it, and would act accordingly. Moreover, quantum mechanics said that you couldn't -- with any certainty -- declare a set order. Instead, you had to settle for predicting probabilities.
On the other hand, if general relativity is correct, then matter couldn't fluctuate so wildly. You would, at some point, be able to know where all matter is and exactly where it's going. Which, again, is at odds with quantum mechanics.
But rest assured that scientists, physicists and armchair experts alike are all desperately trying to find a way to reconcile the two. One front-runner is string theory, which says instead of a particle acting as a dot, it acts as a string. That means it would be able to wave and move and loop and generally do all sorts of stuff that one point couldn't. It could also transmit gravity on a quantum level, and the spread of the particles on a string would theoretically make a less jumpy, less crazy atmosphere. Which opens the theory, of course, to agreeing with general relativity. But keep in mind that string theory has never been confirmed with any experiment -- and there's much debate if it can be proven at all.
If such a monumental experiment were to occur, it would likely happen at a particle accelerator. That's where we might find superpartners. (No, not Batman and Robin). Superpartners are a part of string theory that says each particle has a supersymmetrical partner particle that's unstable and that spins differently (for example, the electron and the selectron or the graviton and the gravitino). Lucky for us, in 2010 we found evidence of our first Higgs boson when crashing particles together in the Large Hadron Collider, so we might be on our way to experimentally proving string theory.
Spin also might help us experiment with quantum entanglement, where electrons get caught in each other's spin. It's easy to see in small spaces, but scientists are working to send photons into space and back to measure how it works over a large distance -- and curvature -- of space and time.
But we also might look to black holes to suss out a Theory of Everything (a TOE!). In a black hole, you have a really heavy thing (a star, which general relativity applies to) and a really small thing (the teeny tiny speck it's crushed into, which quantum mechanics explains). So if we can determine what happens -- or what changes -- when the big gets small, we just might reconcile quantum mechanics and the general theory of relativity.