Tomorrow, NASA launches the OCO-2 satellite, which will make a detailed map of how much CO2 is in the atmosphere at various points on the globe. They plan to combine that data with data from other existing satellites, atmospheric sampling, and ground sampling, with the goal of finding out where CO2 is being produced and where it's being absorbed—in very high resolution, about 3 km2 per measurement, or, smaller than a big coal-fired power plant.
The satellite will be in a polar orbit which allows it to fly over every single spot on earth every 16 days, which means it will generate a complete map of CO2 concentrations every 16 days—less the areas that were covered in cloud when it flew over on that cycle. This repeated mapping also means that seasonal variations can be tracked, to separate a long-term trend from a seasonal fluctuation.
OCO-2 measures CO2 by measuring how much light is absorbed by the CO2 as sunlight travels down to the surface, reflects off the planet, and bounces back up to the satellite. So, cloud cover interferes with the measurement, and repeated mapping is one of the ways they're compensating for that.
It's not the only thing they're measuring, of course. There are several measurements, each complementing the other, to build an excellent picture of what's going on. All of them are spectrometer-based. (There are other satellites already orbiting, and OCO-2 and its data will join them. Each of the other satellites has a different area of expertise and different types of instruments, and they travel together in a group, all measuring the same spot on the planet within minutes of each other.)
Absorption spectra are a way to measure what's in a thing from a distance, without touching it. They're used in astronomy to figure out what's in a star or a dust cloud, in a lab to figure out what an unknown material is, and here, it's used to measure how much CO2 and O2 is in the atmosphere.
The light source for this spectrometer is our sun, whose spectrum is well known, and the satellite measures the spectrum after it's travelled down through the atmosphere, reflected off the surface, and travelled back up through the atmosphere. Along the way, the light has some of its energy absorbed by the molecules that make up the atmosphere. CO2 is the one OCO-2 is interested in, so the satellite will specifically be looking for two spikes that indicate CO2. The deeper the spikes, the more CO2 was encountered in the light's double-trip through the atmosphere. This is a measurement of amount not concentration, however, so if the light bounces off some clouds and doesn't make it all the way to the ground, the light will have travelled through less air and thus interacted with less CO2, measuring a lower amount.
To convert from an amount to a concentration, which is what they're really looking for, the amount of CO2 measured has to be set in a ratio to the amount of air measured. This is why the system also measures O2, which is at a constant concentration everywhere in the atmosphere—21%. This way, if a very low CO2 measurement is taken due to clouds, a very low O2 measurement will be made at the same time, and the ratio will still show the concentration. It'll be the concentration at the top of the cloud instead of down at ground level, but the small quantity of O2 will reveal that.
A late addition, not even described on the OCO-2 website (that I could find) but mentioned in this NASA video is that plants in the middle of photosynthesizing actually glow: they take in photons from sunlight, do their photosynthesis, then release a different coloured photon. You can't see it with your eyes because sunlight overwhelms it, and at night they're not photosynthesizing and thus not glowing, but with a spectrograph you can separate out most of the sun's glow and look only at the colour of light the plant glows with. That means NASA can simultaneously measure the CO2 concentration above a forest or field and how actively those plants are sucking in carbon. This gives them a bonus measurement; not only are they quantifying where the CO2 is coming from and where it's going, they can also see when forests and crops are or aren't thriving, long before the green fades.
This should provide a much more accurate map of where CO2 is appearing and disappearing from our atmosphere. Reported data from producers isn't enough, and there isn't anybody to report on what the plants and oceans are doing. Knowing where it's coming from and where it's going is the first step in improving either of those.