Space telescopes are satellites in orbit around the Earth, just like weather satellites, GPS satellites, or any other kind of satellite. They all send data to devices on the ground via radio waves. If you've got a GPS device, it's receiving location information from satellites orbiting above you! And when you see a hurricane weather report, showing a hurricane a few days out, that imagery is coming from satellites not ground radar.
If you have a remote phone in your house -- one that doesn't have a wire -- it's communicating with the phone's base station using radio waves just like a satellite in orbit communicating with the ground. Deep space probes like the ones we've sent to Jupiter, Mars and Saturn communicate via radio as well, but they're so far away that it takes hours for the signals to get back to us.
Picture data as well as sound can be transmitted via radio waves. It just has to be converted into a digital format. The pictures that telescopes send back are encoded data just like the visual data on your smartphone's web browser, which displays graphics.
The reason to put a telescope in space is that the Earth's atmosphere obscures details of deep-sky objects, even at night: air turbulence blurs things, and Earth's atmosphere partially blocks or obscures many wavelengths which modern instruments can detect. So we put telescopes in orbit above the atmosphere, in order to see things one can't see from Earth (like, say, the center of the galaxy, planets in orbit around other stars, or details in other galaxies.)