Author
The Apostle Paul identifies himself as the author in verse one (the Book only contains one chapter). He also identifies Timothy as a co-author, though this inclusion is likely honorary. The Epistle is written in first person singular.
Date
There is wide agreement that this Epistle was written between about 60 and 62 AD while Paul was under house arrest in Rome (Acts 28:16).
Occasion
Paul was a prisoner at the time of writing (vs 9), likely in Rome. Thus the Book of Philemon is numbered among the Prison Epistles (Ephesians, Philippians and Colossians being the others.) Philemon (an individual) is identified as the primary recipient. Two other persons are named as well as a local house church at Colassae (see Colossians below). Verse 19 indicates that Paul had led Philemon to the Lord, establishing how the two knew each other. Philemon was likely in a leadership position at this house church.
Paul writes Philemon regarding Onesimus (vs 10), Philemon's slave (vs 16) whom the text implies had run away (vs 15) and had possibly stolen money or property (vs 18). Paul, by the Holy Spirit, had converted Onesimus to the faith while in prison (vs 10) and was writing Philemon to encourage him to receive Onesimus back, forgiving him as a brother in the Lord (vs 16).
Overlap with the Book of Colossians
Evidence indicates that Paul wrote Colossians and Philemon at the same time. Paul lists Timothy as co-writer in both letters (Colossians 1:1, Philemon 1). Paul mentions Onesimus in both writings, and from Col 4:9 we can infer that Philemon and Onesimus lived in Colissae.
Additional evidence linking Philemon and Colossians together is as follows:
As in Phm 1 Paul tells the Colossians he is in prison (Col 4:3)
In both works Paul sends greetings on behalf of Epaphras (Phm 23 & Col 4:12) - the greetings are intended for several common recipients:
Archippus - Phm 2 & Col 4:17
Mark - Phm 24 & Col 4:10
Aristarchus - Phm 24 & Col 4:10
Demas - Phm 24 & Col 4:14
Luke - Phm 24 & Col 4:14