wish I had written down the name, etc. I'm pretty sure it was on PBS, and was a rerun. Possibly this:
http://www.pbs.org/wgbh/pages/frontline/heat/The short answer to "how do we know" is this: carbon isotopes. C-14, a natural radioactive isotope of carbon, decays with a relatively short half-life. Fossil carbon (coal, oil, gas) contains very little C-14, since it has had time to decay. CO2 from volcanoes is likewise depleted in C-14 (IIRC). Burning of more recently formed biomass (from tropical deforestation, etc.) returns C-14 to the atmosphere, but there is not much observed increase in C-14 in the atmosphere. So the increase in CO2 must come largely from "old" carbon, either volcanoes or fossil fuels. Fossil fuels are derived mostly from plant matter, and plants preferentially incorporate C-12 vs C-13 (both stable, i.e. nonradioactive, isotopes). Thus burning either fossil fuels or recent biomass would increase the C-12/C-13 ratio. This is what is observed, without the accompanying C-14 that recent biomass would release. Only burning fossil fuels could lead to the observed changes in isotope ratios.
This is far from the only evidence -- in fact, even without isotope results, the evidence is convincing -- but it's a particularly tight argument. The fact that independent lines of evidence all lead to the same conclusion is pretty overwhelming. Further evidence is only going to lead to refinements in the predictions of decreasingly relevant magnitude.
Note that there's an "advanced" option at the site:
http://www.skepticalscience.com/its-not-us-advanced.htmOh, and there's an 11th fingerprint now:
http://www.skepticalscience.com/Paper_Archives_Reveal_Pollutions_History.html