How are we able to communicate with our spacecrafts so far away? (eg.New Horizons)
The Voyager spacecraft use 23-watt radios, which is higher than the 3 watts a typical cell phone uses, but still a low-power transmitter [2]. The key to receiving the signals is a combination of very large antennas, directional antennas that point right at each other, and radio frequencies without a lot of man-made interference on them [2]. The antennas that the Voyager spacecraft use is 3.7 meters in diameter, and transmits to a 34 meter antenna on Earth [2]. The Voyager antenna and the Earth antenna are pointed right at each other, and when you compare your phone's stubby, little omni-directional antenna to a 34 meter directional antenna, you can see the main thing that makes a difference! [2]. The Voyager satellites are also transmitting in the 8 GHz range, and there is not a lot of interference at this frequency, so the antenna on Earth can use an extremely sensitive amplifier and still make sense of the faint signals [2].
The computers on NASA's robotic explorers are small and lightweight, and they use weak radio signals to communicate with Earth [1]. The Deep Space Network uses antennas located all around the world to detect and boost these signals [2]. The station with the largest antenna, in Canberra, Australia, can communicate with objects as far away as Voyager 2, which is currently exploring interstellar space [2]. The DSN antennas are able to receive weak signals from these far-off objects and boost them to a level where they can be "heard" by the scientists on Earth [2].