Obviously, Paul had a close relationship with both the slave Onesiums and his owner Philemon. Some scholars believe that Onesiums first heard about Christ when he shared a jail cell with the apostle (see verses 9-10). As you read Philemon, look for clues into Paul's relationship with each person.
Philemon gives us a model of Christian diplomacy. As you read it, think of awkward social situations you know about: two estranged friends or a parent-child conflict, for example. Notice the kind of persuasion used by Paul, and try to apply it to your own circumstances.