The planet will be in the habitable zone around a red dwarf – a sweet spot where liquid water can remain stable on a planet's surface. The zone will be only a fraction the distance from the cool star as Earth's habitable zone is from our hotter Sun.
For those planets with orbits tilted edge-on to Earth, detecting them will be straightforward. Astronomers will see if the star dims slightly when the planet passes in front of it, or transits.
A planet in the habitable zone of a red dwarf would complete its racetrack orbit in just two weeks. This would allow multiple transits to be observed quickly. Also, because it is so close to the red dwarf, a planet is more likely to be in an orbit aligned along our line of sight, and will be more likely to be discovered transiting.
But there is one big catch. Young red dwarfs have a petulant youth stretching over billions of years. Titanic stellar flares erupt without warning and blast out lethal doses of ultraviolet radiation. Ocean life on a planet may be safe from the UV just a few feet underwater and still extract enough light for photosynthesis. But anything living on the surface could get fried without a liberal coating of Sunscreen 2000.