In the 18th century, the distance to the Sun was measured using the transits of Venus. Nowadays, the timing of radar pulses is used to measure the distance of things in our solar system. What instruments are used to perform these measurement? What do they look like (bonus points for pictures)? Are there observatories with "radar guns" dedicated to measuring the distance of the Sun?
They look like radio telescopes, because that is what they are.
Some radio telescopes have been outfitted to transmit rather than receive, requiring using a different radio telescope to receive the reflected signal. Other radio telescopes have been outfitted to transmit as well as receive in a pulsed manner. These can be used for radar astronomy without the help of a separate transmitter.