How could Jesus' audience hear Jesus without audio installation? I am wondering, today we use microphones and large sound systems to amplify someone's speaking. How did they do that 2000 years ago? Jesus spoke outside regularly before large crowds of people. I expect there were enough children, and disagreeing people, so it wasn't always quiet. Your voice won't reach very far when there are a lot of people, especially when there is a kid crying or someone having a discussion. 

My question is: 

How did the people back then hear Jesus' (or anyone else) preaching when there was a large crowd?
You are right, communication before modern electronics relied more on the speaker yelling and a crowd who surrounding attentively.  Consider the ancient Roman coliseum for example. This place could house an audience of 50,000+ and people would need to shout loud to the crowd and be heard.  

When we imagine the crowds that Jesus spoke to a typical Jesus movie seems to portray it right. Sometimes crowds followed him to a place where he could be heard well, like for the sermon on the mount.  Other times they pressed in on him and he even had to sort of hurry away so that it did not become too chaotic. Also many would be responding and discussing among themselves what the meaning was for something he had said. In these conditions many would not hear exactly what was said and only get bits and pieces.  There is also the repetitive second hand reiteration of what he had said. For those who could not hear they would listen to the stories told by others, even late into the night throughout the towns where Jesus preached. 

Then there is the example of the Baptist preaching by the river. Have you ever yelled in a valley and heard the echo carry your voice seemingly for ever?

In summary, one could definitely communicate to large crowds in ancient Rome, such as for entertainment in the amphitheaters or when generals gave pre-battle speeches for example. When large crowds were addressed, sometimes good places were chosen for the acoustics, and the crowd would be more aware of when to hush for the communication to be effective. Even making a makeshift blow horn with your hands could have been used as ancient Greek actors already had horn shaped mouths in their masks for this purpose. However, there would certainly be some, especially among noisy crowds, who could not hear and would rely on what others said.