Deep space probes have radio transmitters and high -gain directional antennas aimed at Earth through which they send telemetry and science data, including the images captured by their onboard camera(s). These radio signals are received on Earth by the huge (70 m) radio antennas and sensitive receivers of NASA's Deep Space Network, with facilities located in Australia, Spain, and the US.

With radio waves. An antenna on the spacecraft sends a directed beam of radio waves towards Earth where another antenna receives it (typically one of the Deep Space Network). The data rate decreases with increasing distance, but it's enough to transmit images over billions of kilometers if you have enough time. New Horizons needed over a year to send back all the data it took during the Pluto fly-by. We still have contact to the Voyager spacecraft, 20 and 23 billion km away. Saturn is "only" about 1.5 billion km away.

There are some experiments with laser links for interplanetary communication, we might see these being used in the future.

Radio waves, Light we see, ultraviolet, Xrays are all the same thing. We can see light, Xraay machines can see and record x-rays, but instruments on earth can also see the special Radio wave light beacon on the spacecraft from very far away. It's hard to block and doesn't take a lot of energy to transmit compared to a lot of other special types of lights. The light blinks on and off very rapidly. The antannae on earth see it and convert the ons and offs into 1s and 0s. DATA!

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The information travels via waves on the electromagnetic spectrum, which in theory can travel an infinite distance unless something interferes with it (reflection, attenuation, etc). It's just a matter of time for it to travel whatever distance it needs to go.