How does relativity...work? I understand the principles of relativity. I understand why we need relativity if we are to have the laws of physics be the same in all inertial frames. But physically speaking, how does relativity actually work? In particular, I was thinking about length contradiction, and I don't understand how moving objects shrink. I understand why they need to, just not how. Is the fabric of spacetime bending in some weird way around a speeding object in order to shrink the object? (Presumably, this might make sense, since massive objects warp spacetime, and fast moving objects have a large relativistic mass). Is this explainable using general relativity? 
Edit: To elaborate, my question is more about the mechanics of what is happening to make the object appear shorter. For example, consider a straw in a glass of water, and a straw not in a glass of water. In both cases, the straw is the same. However, it looks weirdly disjointed when in the glass of water; from a new perspective, it looks different. However, there is a good explanation for why this is; the light refracts when changing mediums, and this thus changes your perception. I'm looking for a similar explanation as to "how" the perception that something has changed length actually comes about in S.R. –
 A: The object does not physically shrink. Its length appears to change when viewed from a moving reference frame. You must remember that the effects of relativity are symmetrical. If a fast moving spaceship, and all the people in it, seem to have contracted in length from your perspective, from their's it is you who is fast moving and contracted. 
The effect comes about in a way that is precisely analogous to a rotation of spatial coordinates. If you have a 3D coordinate system that is rotated relative to mine so that your axes point in different directions to mine. We will now disagree about the coordinates of any point in that space. Moreover, if we consider two points in space, we will disagree about the horizontal and vertical distances between them, for example. The same effect occurs in spacetime. Observers that are stationary relative to each other each have a time axis pointing in a common direction, but if they start to move their time axes diverge so they are no longer pointing in the same direction in 4D space, which causes them to disagree about positions and separations in time.
A: It shrinks for simultaneous (according to your own clock) readings of a your meter stick at both ends. Given that the object is in a different frame, the measurement cannot be simultaneous to it's clock, and will furthermore be of a not contracted length. So you have a "shorter" time displacement and you should have as a consequence a shorter spatial displacement, because the overall space-time difference must be agreed between you and the thing.
So, simultanous in our frame means $$\Delta t = 0$$. But $$-c^2\Delta t^2+\Delta x^2 = \Delta x^2 = -c^2\Delta t'^2+\Delta x'^2$$. So it must be that 
$$\Delta x'^2 > \Delta x^2$$
A: Suppose you're in Chicago, facing New York, which is 800 miles straight ahead.  
Now turn ninety degrees to the right.  All of a sudden, New York is 800 miles to your left!
How did New York manage to shift its position so dramatically all of a sudden?
The answer, of course, is that it didn't.  What changed is your description of New York's location, which switched from one perfectly valid description ("800 miles straight ahead when I face east") to another ("800 miles to my left when I face south").  
That's just what happens in relativity.  There is no one correct answer to "how long is the meter stick?" any more than there's one correct answer to "which direction is New York?".  The direction of New York depends on which way you're facing.  The length of the meter stick depends on how fast you're traveling with respect to that stick.  Neither New York nor the stick needs to know anything about this, or to adjust itself in any way just because you changed from one description to another.
A: It's just a math model, it's not necessarily literally describing reality. You can interprete it that way in some instances if you want to. I don't think that any of the special relativity effects have been observed directly and explicitly.. 
