So Brogi and his colleagues have proposed a way to help separate those two sources of light. Because the planet is moving around the star, it is also moving toward, and then away from, the Earth throughout its orbit. When a source of light moves toward an observer, the light waves become compressed; when the source moves away from the observer, the light waves become stretched out. This is called the Doppler effect, or redshift. It also happens with sound waves, which is why when a police siren is moving toward you, it sounds like it is increasing in pitch; the waves get pushed together so that they literally have a higher frequency. When the car passes you and starts moving away, it sounds like the siren is getting lower in pitch, because the waves get stretched out and the frequency goes down.
The idea is that, out of the sea of light coming from a distant star, scientists could pick out the island of light coming from the planet by looking for the redshifted/Doppler shifted light. (This also could be used to separate any interference from Earth's own atmosphere.) Looking for those shifts in the light also falls under the header of spectroscopy.
Nonetheless, the Doppler shift approach wouldn't be powerful enough to work on its own, and this is where the second technique comes in: Astronomers would need to directly image the star or planet system first.
The planet-finding technique known as "direct imaging" is pretty much what it sounds like: an attempt to get a direct snapshot of both a planet and the star it orbits. To do this, scientists try to reduce the star's blinding glare enough so that they can see the light from the planet. It's a challenging method and one that can't be done for just any system — the planet has to be sufficiently bright compared to its parent star, which means most of the planets seen with direct imaging thus far are gas giants like Jupiter, and oriented in such a way that it can be viewed clearly from Earth. 
So Brogi and his colleagues proposed the method of first directly imaging the planetary system, using that image to locate the planet, and then further separating the planet's light from the star's light using the Doppler method. From there, they can use high-resolution spectroscopy to learn about the planet's atmosphere.
Telescopes currently in operation don't have the sensitivity to make this plan a reality, but some very large telescopes currently under development could. These scopes should be able to directly image smaller planets, as long as those planets are orbiting dimmer stars. Those include the Giant Magellan Telescope, scheduled to turn on around 2021, and the European Extremely Large Telescope, set to begin taking data as early as 2024. Direct imaging capabilities are likely to improve by leaps and bounds with these telescopes, but with direct imaging alone, it will likely not be possible to characterize many Earth-size, potentially habitable worlds.
During his talk, Brogi said there should be "on the order of 10" potentially habitable planets that this method could identify and study.
Brogi noted that there are caveats to the plan. For example, many of the predictions that he and his team made about how sensitive the method would be were "based on best-case scenarios," so dealing with real data will undoubtedly pose challenges. Moreover, the method compares the observed planetary spectra with laboratory experiments that recreate the expected spectra for various chemical elements, which means any errors in that laboratory work will carry over into the planet studies. But overall, Brogi said he and his colleagues think the approach could provide a better glimpse of the atmospheres of small, rocky, potentially habitable planets than scientists are likely to see for a few decades.
They aren't the only group that thinks so. Researchers based at the California Institute of Technology (Caltech) are investigating this approach as well, according to Dimitri Mawet, an associate professor of astronomy at Caltech. Mawet and his colleagues call the approach high dispersion coronagraphy (HDC) — a combination of high-resolution spectroscopy and high-contrast imaging techniques (direct imaging). (Similar lines of thought have been proposed by other groups.)
Mawet told Space.com in an email that he and his colleagues recently submitted two research papers that explore the "practical limits of HDC" and demonstrate "a promising instrument concept in the lab at Caltech." He said he and his colleagues plan to test the technique using the Keck telescope, located in Hawaii, "about two years from now," to study young, giant planets (so not very Earth-like). He confirmed that to use the technique to study small, rocky planets like Proxima b, scientists will have to wait for those next-generation, ground-based telescopes, like the Giant Magellan Telescope and the European Extremely Large Telescope. He also confirmed Brogi's estimation of "on the order of 10" rocky exoplanets in the habitable zone of their stars that could be studied using this technique.
"As [Brogi] mentioned, there are several caveats associated with the HDC technique," Mawet told Space.com. "However, we are working on addressing them and, in the process, studying the fundamental limits of the technique. Our initial results are very promising, and exciting.