Basic chemistry, that's all.
Carbon has five isotopes if you count the basic form, Carbon 12, which makes up about 98.9% of all carbon found on earth. C14 is the one you're probably already familiar with, given its use in dating how old objects in archaeology and anthropology are. C13 is the stable isotope, unlike C14, its radioactive brother, but both make up a tiny fraction of all the C out there in the natural carbon cycle.
http://www.chemicalelements.com/elements/c.htmlWhat scientists know is this - going back for thousands and thousands of years, the relative levels of these isotopes in the natural carbon cycle of plants and animals growing and dying and decaying has remained pretty much the same. They know this from testing glacial cores and snow and ice samples and sediment and fossilized animals and plants and the whole nine yards.
That is, the relative levels were pretty much the same until about 1750 or so, which is when we started burning lots of stuff as the Industrial Revolution got underway. First wood, then coal, now oil and gas, burned in huge quantities emitted enormous amounts of anthropogenic carbon into the atmosphere.
We know this with an even higher degree of specificity thanks to Roger Revelle and Charlie Keeling. It was Revelle who suggested during the IGY that scientists collaborate to take daily samples of atmospheric trace gases. He believed that the amount of C in the atmosphere was rising thanks to human activity and Keeling would prove him right. Since 1958 until today, every day, scientists around the world have sampled the air and found ever-higher amounts of C in the air.
What's definitive, though, is the isotope ratios. In recent years, the ratios of C13/C12 has declined substantially, and not coincidentally, the carbon contained in fossil fuels has a far lower ratio of C13/C12. On top of that, C14, though already a trace gas of a trace gas, has declined substantially as a percentage of the atmosphere since we began to burn fossil fuels in earnest. Fossil fuels, tens and hundreds of millions of years old, contain no C14, since it long since finished the process of radioactive decay. Finally, the amount of oxygen in the atmosphere is declining - since it's been displaced by billions of tons of CO2 we produce.
http://www.carleton.edu/departments/geol/DaveSTELLA/Carbon/carbon_intro.htmThere's also this excellent analysis from Daily Kos, of all places.
http://www.dailykos.com/storyonly/2006/7/7/104649/4911