How did Paul deliver people to Satan?

Paul singled out a man having sex with his father's wife in 1C 5:

4 When you are assembled in the name of the Lord Jesus and my spirit is present, with the power of our Lord Jesus, 5 you are to deliver this man to Satan for the destruction of the flesh, so that his spirit may be saved in the day of the Lord.

Click to expand...

1. Do it with the power of our Lord Jesus.
2. Deliver him to Satan.
3. Hopefully, he would learn the lesson and repent.

Another example in 1T 1:

18 This charge I entrust to you, Timothy, my child, in accordance with the prophecies previously made about you, that by them you may wage the good warfare, 19 holding faith and a good conscience. By rejecting this, some have made shipwreck of their faith, 20 among whom are Hymenaeus and Alexander, whom I have handed over to Satan that they may learn not to blaspheme.

Click to expand...

Hymenaeus and Alexander were once in the faith, but they failed to hold on to it.

How exactly did Paul go about delivering or handing people over to satan?

Excommunicate them. This would remove them from the fellowship and protection of the church.

How would Satan deal with them in such a way for the destruction of their flesh or so that they may learn not to blaspheme?

They went back into the realm of the world. Satan was the ruler of this world. If they still had some conscience left, the pain and the destructive consequences of sin could serve as a wake-up call, leading them to recognize their need for repentance and reconciliation with God. He might remember the good old days when he had fellowship with God and with the church.