I never cease to be amazed by the number of people who will insist that observable facts are non-existent, if these offend their sense of economic rightness. Yet global warming is easily observable, all over the planet, from the loss of days of winter to the melting of both mountain and icecap glaciers. And the interesting point is that the physics of global warming have been well understood since early in the twentieth century; the only question left was, whether and how much we were affecting the atmosphere in ways that would contribute, a question that has only been recently answered.
Start with the earth's heat budget. The sun, at several thousand degrees Kelvin (1), radiates like a black body whose most intense wavelength is that of visible light (actually, somewhere in the green). Most of this light radiates off into space; a tiny fraction is intercepted by the earth, with a cross-section of around 200 million square miles. Some of the light that reaches earth immediately bounces off snow caps or cloud tops into space, and does not contribute to the heat budget; but the rest, reaching the ground, is absorbed, heats up the ground a bit, and the warmer ground then heats up the lower atmosphere.
Now for a simple rule to understand: as much heat as is absorbed by the earth from the sun every twenty-four hours has to be radiated back into space in that same twenty-four-hour period. Otherwise, the earth will continue to heat up, very, very fast, and we will all quickly be turned into crispy critters in a process that will make actual global warming look like a cool winter day.
The earth, like the sun, radiates like a black body, but since its temperature is so much lower (around 300 degrees Kelvin compared to several thousand for the sun) its highest level of radiation is at much longer wavelengths, namely those of infrared radiation or heat.
The interesting point is that certain gases in the atmosphere, ones that have slightly more complex than normal molecular structures — carbon dioxide and methane spring immediately to mind — tend to absorb infrared waves at certain wavelengths or bands of wavelengths. They don't hold onto this extra energy forever, but reradiate it away at these and other wavelengths, so that these heat waves can go on their merry way. The problem is that the molecules in question don't necessarily reradiate them in the same direction they were going in the first place; they are just as likely to head right back down towards the earth, where they will have to be radiated away again. If you increase the number of molecules of these somewhat complex "greenhouse gases" in the atmosphere, more and more heat gets recycled within the atmosphere rather than being radiated back out into space.
The result? Remember the 24-hour rule? Well, what happens is that not all the heat arriving from the sun in that 24-hour period gets radiated back away in the same 24-hour period.
So why haven't we turned into crispy critters yet? Luckily, there's an easier solution. As the earth warms up a bit, it radiates more heat waves, and so, even though more get caught by the greenhouse molecules, more also escape into space. By the time the temperature of the surface of the earth and atmosphere rise by a tiny fraction — say, a couple of degrees Kelvin (significantly less than one percent of the baseline temperature of earth and atmosphere), the heat budget is back in synch and we are all saved from being turned into charcoal.
Again, this process has been understood since the early twentieth century, and the only problem with extrapolating it to man-caused global warming was the assumption that we were not significantly affecting the number of greenhouse molecules in the atmosphere — an assumption which has turned out, over the past few decades, to be wildly optimistic.
So, since we are obviously not going to be burnt to a crisp, should we worry? Yes, because our oceans and atmosphere are very sensitive to such tiny changes in temperature. They may make the difference (to choose an obvious example) between having a part of the earth covered by solid H2O and not having that, which in turn will affect the earth's albedo, allowing significantly more solar radiation to be absorbed by the earth, which in turn will cause even higher temperatures before the heat budget is in synch again.
We are in a bad way. It's small comfort to realise that things could be much worse.