They use giant dishes and a lot of signal filtering. The farther the system they are communicating with, the slower the bit rate they can communicate at. Your home internet connection is probably in the tens or hundreds of millions of bits per second. Extremely distant probes have much slower rates. The New Horizons probe had a connection speed of approx. 38 thousand bits per second when it went near Jupiter. By the time it was at Pluto that rate had dropped to 1 thousand bits/second.
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