For an exercise in fiction writing, record a few minutes of casual conversation between two people and then type it all out. Very quickly you’ll notice that most people don’t converse in carefully measured prose.
No, they interrupt each other. They talk over each other. Speak in fragments. Go off on tangents. They repeat themselves. Repeat themselves like crazy. One person may mis-hear what the other person just said, or miss it entirely because they are caught up in thinking what they are going to say next. Or because the other person was muttering.
Try the same exercise with a three-way conversation and it gets even wilder.
There’s no way you’d ever want to write dialogue like that. Such faithfulness to reality would be excruciating to read. What you can do, though, is use reality as seasoning to give your dialogue some savor.
If you look back through your dialogue and it reads like something out of an annual report to the board of directors, turn a few of those long, elegant sentences into fragments. Have one character interrupt another every now and then. Let them wander away from the main topic for a sentence or two, then bring them back.
A little of this goes a long way. If you go overboard, your characters may start sounding like Grandpa Simpson explaining about that time he caught the ferry over to Shelbyville to get a new heel for his shoe, and how he tied an onion on his belt, which was the style at the time.
But if you sprinkle an interruption here, a tangent there, and a fragment over on the next page, your characters will sound more human.