“But I tell you who hear me: Love your enemies, do good to those who hate you,  bless those who curse you, pray for those who mistreat you.  If someone strikes you on one cheek, turn to him the other also. If someone takes your cloak, do not stop him from taking your tunic.  Give to everyone who asks you, and if anyone takes what belongs to you, do not demand it back.  Do to others as you would have them do to you.
“If you love those who love you, what credit is that to you? Even ‘sinners’ love those who love them.  And if you do good to those who are good to you, what credit is that to you? Even ‘sinners’ do that.  And if you lend to those from whom you expect repayment, what credit is that to you? Even ‘sinners’ lend to ‘sinners,’ expecting to be repaid in full.  But love your enemies, do good to them, and lend to them without expecting to get anything back. Then your reward will be great, and you will be sons of the Most High, because he is kind to the ungrateful and wicked.  Be merciful, just as your Father is merciful.
It is one of the key points to Jesus’ ministry and Paul to follow, Love. Jesus did not just say love your family, love your God, love your church and friends, he said love your enemy. We are to love those who seek to do you and your family harm. You are suppose to not only pray for them and resist the urge to hurt them or speak speak ill against them, but to actively try and help them.
Why should we do this? Well for one Jesus said we should do good “without expecting to get anything back.” The other verse to answer your question is at the end of 35 and verse 36. Your Father in Heaven has been kind to those who are “ungrateful and wicked”, you should too “just as your Father is merciful.”
Exactly who are your enemies? These are not the people you dislike (although you should treat them with love as well), but those who hate and despise you. We are to wish for their well being whether it hurts you or not. Remember more often than not these enemies are lost. These lost souls are what we are down here on this Earth for. We are to try and steer them to the only person who stepped foot on this Earth who can, our savior Jesus Christ.
Jesus forgave and prayed to his father to forgive those who had sentenced him to die and those who carried it out. That is true love. Jesus looked to the ones that wished him the most harm and without them asking, forgave them.
How can we do this? We should seek to do good. We should actively seek out a way to help those who would do us harm. We should also bless them, instead of complaining about your enemy. One of the best things you can do is to pray for them. While you are blessing your meal or thanking God for all he has done in you life ask the same for your enemies.
Remember in the end it is an opportunity for Jesus to save another soul. By inviting your enemy to church instead of pushing them away with negative words and actions, you seek to bring another lost sheep into the fold. Jesus has the power to turn enemies into brothers and sisters.