Concerned reader Azzle writes: "If matter can neither be created nor destroyed then how can the universe expand? That is to say, from my understanding of the words I just used and no knowledge of the math behind them, if the universe is expanding then I assume somehow it's getting bigger or less dense and therefore wouldn't it be filled with more matter that didn't previously exist? Is my tiny reptile mind missing something super obvious about this? Anyway good luck explaining the cosmos to me, at the very least it should make a good entry for your blog."
Thanks, Azzle, for asking a really tough question. The difficulty of answering this can quickly spiral out of control, so for my own sake I'm going to stick to answering exactly what he's asked and not much more. However, since Azzle's question hits really close to questions about the most fundamental nature of our reality, I'll refer you all to some guides written by others much more versed in this topic than I am. At the very least, even if I get everything wrong I'll get to post some pretty space-pictures.
Alright, what's happening to the density of the universe? Normally density is a pretty straightforward quantity; you find the mass of an object and divide it by the amount of space it takes up. Well, this time it's a bit more complicated because the object we're talking about is actually space itself. Take a minute: space itself. Our universe is all there is – as far as we know, we can't sit inside some super-universe and wrap a tape measure around our universe's waist. The only thing we can use to measure the size of the universe is the universe itself, and the space inside it. If you imagine that your ruler were made of rubber and it kept shrinking and stretching, you'd get a crummy analogy for this situation. There are a couple better ones:
My favorite is the "raisin bread model" - the universe is a loaf of raisin bread in the oven, and the raisins are the galaxies. As the bread rises, the raisins get further apart. There isn't any more bread than there was before, but it takes up more space.
There's also the "ants on a rubber band" model. If you have a bunch of ants crawling on a rubber band and you stretch it, the ants will get further apart even as they continue to march relative to their spot on the band.
The best analogy, though, is probably the balloon. Imagine that you live on the inside (outside works, too) of a balloon. You draw two dots on the skin and connect them with a line, saying, “I declare this length to be one foot!” Unfortunately for you, the balloon is hooked up to a helium tank and starts inflating. All of a sudden, one foot is a lot bigger than it used to be! Well, apparently the universe is kind of like that, except in four dimensions (three space, one time). Also, the balloon skin is a 2-D surface expanding into 3-D space, but the universe doesn't expand into anything. There's just more space than there used to be.
The balloon is also good for another purpose: understanding how there can be no center. A common, wrong way to think about expansion is as if 14 billion years ago there were a big explosion that sent pieces flying everywhere. If this were true, we could look at everyone's direction of motion and work backwards to find the middle! Unfortunately nature chooses to take the confusing route on this one, and we have to get back to the balloon. If we all live on the surface of a balloon, as the balloon gets bigger all the galaxies move away from the Milky Way at a speed directly proportional to their distance. Great, this tells you exactly the same thing as the "exploding" version. The difference is that on the balloon you also can't point to any one spot and say it's the center, and this agrees with one of the most important observations ever made of the sky, which tells us that space is the same everywhere we look - no place is uniquely different from any other.
To answer your question, “How is the universe expanding?” the best I can do is say it's a higher-dimensional balloon being blown up. There's an obvious question that I'm not going to even touch - “Why is it expanding?” Why does the universe decide to get bigger instead of smaller, or just stay the same size? Well, this is a pretty hotly contested question and something the LHC will hopefully be able to chip in on; these folks can tell you all about it. Me, I know when I'm in over my head, but I can give it a shot if requested by popular demand.
But Azzle doesn't care about mundane questions like “is the universe going to keep expanding forever” or “How can it not be expanding into anything that makes absolutely no sense,” the only thing Azzle cares about is density. And that's the only thing I'm going to answer. What's happening to the density of the universe as the space inside of it gets bigger? Well, the all-knowing Wikipedia says you're exactly right: the density is decreasing, and eventually other galaxies will be so far away that they'll be too faint to detect. Carried to extremes, this leads to the “cold death” scenario of an open universe. But fear not! We could also all die in the Big Crunch, if the universe is closed, but if we're really lucky then there's just enough matter to balance out the expansion and we'll live happily ever after in a flat universe. Strangely enough, from what we can tell today the universe is eerily close to being flat.