Jesus told the crowd, that the one who is without fault should be the first one to throw the stone. Obviously, since no one was without sin, nobody threw the first stone. And they dispersed.
It is a little deeper than that. Note that the Pharisees were attempting to trap Jesus by presenting Him this case.
The Law of Moses said that the woman could be stoned, but Roman Law prevented the Jews from actually stoning her.
They figured Christ could do one of two things.
- Deny the Law of Moses - In which case, they could use that against Him with the people. After all, how could the Messiah deny the Law of Moses.
- Say to Stone the Woman - In which case, they could then take the case to the Roman authorities claiming that the Nazarene advocated violating Roman Law.
Christ was more subtle than that. He told the Pharisees they COULD go ahead and stone her!!
The Pharisees viewed sin and either conforming or violating the prescripts of the Law, since they rigourously followed the Law, they were sinless (as they and the Jews percieved sin)
But He said it in a way that would be laughted out of Roman court.
So the Pharisees had no case, Christ neither denied the Law of Moses, so they could not claim that to the people, and they could not bring him to court under Roman Law.
That is why the elders, the wisest of them, left first. They saw how Christ escaped their trap.
As far as stoning her, they could not do so under Roman law, at least not without risking Roman reprisials. They might be able to get away with it for a disturper of the peace (such as Stephen), but for a simple adulteress, the Romans would see that as an affront to their authority.
So they were not going to stone her at all, just use her as bait for the trap.