Does Paul teach anything in his epistles about how to cast out demons?
No, Paul's epistles contain no teaching on how to cast out demons. He gives no instruction for exorcism and is silent on the practice. The only related directive is to lead someone into the plan of salvation, not to engage in casting out demons.
Les explains that during the early Acts period none of Paul's letters had been written yet. Later, when Paul wrote his epistles, they became the Word of God, but in them he never gives instruction for exorcism. Les says he cannot find Paul teaching how to cast out demons; Paul is silent. Les personally thinks believers should leave it alone aside from leading someone to salvation, and he notes that involvement with demonism destroyed the ministries of some he knew.