How/why does gravity affect spacetime? I've always heard that gravity warpes spacetime, but I've never understood why and/or how. I'm only 12 so please keep it simple if possible. 
 A: Put a quarter in a funnel. Then look at it from above.
See how it is curved on the funnel part but not on the quarter? That's what a big ball of gas looks like. The spacetime outside the gas is curved, but the spacetime inside is less curved.
Now remove the quarter and put a smaller coin like a nickle or a dime in the funnel. This time there is more region of curvature outside the coin. That's what happens outside a ball of gas as it collapses.
The regular vacuum curvature, the way spacetime can curve away from energy or matter can extend further towards the surface because the surface is farther in. And yes, spacetime can curve even in vacuum.
For a more realistic example you could take two funnels of different curvature and make a copy of each of them. So you have two bigger curvature ones and two smaller curvature ones.
Cut one bigger curvature one at a circle of diameter 6cm , and cut the one smaller curvature one at a circle of diameter 6cm and attach the bigger curvature one's outside to the smaller curvature one's inside.  That's a star with more curvature on the outside and less on the inside. They line up and the change in curvature type is based on how much matter there is at that layer (how much matter is at the circle of diameter 6cm). So what matter does is allow two different types of curvature to line up with each other.
Now repeat with the other ones funnels. But this time cut it at a diameter of 5cm. This corresponds to a smaller star where the outer layer has compressed inwards over time.
That old larger type curvature now extends farther inwards becasue it keeps going until it meets some energy or matter.
By using more funnels of weaker and weaker curvature you can smooth it out, with a small coin in the center. Just treat each inner funnel as an outer funnel and cut the inside last out and put a less curved funnel inside until the inner most one has a small coin.
Each transition from a bigger curvature funnel to a smaller curvature funnel happens in a place where matter and energy allows different types of curvature to line up.
But curvature is natural and happens even in empty space.
A: 
I've always heard that gravity warpes spacetime,

This is putting the cart before the horse. What you should have always heard, if space time is in the vocabulary, that the energy momentum tensor  in space time generates gravity.
"Energy momentum tensor" is a mathematical way of saying that mass generates gravitational behavior, a mathematical model. This  differs from Newton's model, which says that mass generates a gravitational field. 
The difference is in the mathematical formulation, but it is important enough to have measurable differences for large masses and large distances. Both theories coincide for small masses and kilometer distances, but even for planetary distances general relativity, the energy momentum tensor model, predicts behaviors that have to be taken into account for the GPS system to work correctly.
And as one has to repeat about physics theories, they are mathematical models. The models tell us how mathematics can fit observations and, important, predict correctly new observations. They can tell us how from the assumption that gravity is the effect of space curvature we can describe the orbits of the planets with great accuracy. The models cannot tell us why there are planets and energy and momentum. These are observational facts.
A: Once you change your statement to "mass warps spacetime and warped spacetime means we get gravity", everything will make sense.
Essentially, having mass in the space (or/and energy, doesn't matter much for this discussion) changes how distances between neighboring points in space behave. Because space-time is "squished" where the mass is and flat(normal) far away from the mass, and these two have to somehow match in the middle, the effect of this "squishing" extends from the particle (with smaller effect over distance). So that's how gravity works at a distance. How exactly that happens is governed by Einstein's equation (which was many times experimentally verified to give correct predictions).
Why mass does that to space-time is more of a philosophical question. It's just how our universe turned out to be.
As to why warped space-time creates gravity, it's just from the distances themselves. Try doing this: (1) go step forward, then step right. (2) first step right, then step forward. In a flat space, you'll end up in the same position on both tries. In a curved space, this is no longer true. The same happens in time (for this reason, imagine every point also having its own clock): (1) stay here for a second, then move forward. (2) move forward, then stay for a second. You may arrive at a different point or/and at the different time on the clock at the place where you are. That's all that "curved space-time" means. You may imagine a rubber sheet with a heavy ball on it, which is usually used to illustrate the effect of extending the distortion away from its cause, and the curvature itself.
Now the easy part... we don't have to know anything new about gravity. Physics does whatever you know it does... but the outcome changes. An object doesn't know or care about the curvature... a planet just continues on straight (remember: there are no other forces, and gravity doesn't count as a force now because its effect is in the curvature of the space-time itself). But step straight forward+step in time+step straight forward+step in time... no longer makes a long straight line! The space is curved, so the "straight" (the shortest way from one point to another) is a curve. In the case of planets, an ellipse (more or less a circle around the Sun).
I hope this answers your question in an easy to understand way.
