What can the parable of the prodigal son teach Christians about how they should act towards sinners?

it teaches them how we should forgive sinners. If you've read the prodigal son properly and understood the message you'll see that although that the son sinned the father forgave him that is the message it shows to Christians. It is also showing the affects of jealousy and how the older son felt when he did all the hard work and the father gave his son a feast for returning home.