Nowhere are we told that he prayed or took authority over territorial spirits when he entered a town. The reason is that he already had the Holy Spirit and the gospel and it was the gospel that overthrew the power of the spirits. He did cast out demons once or twice as part of a healing ministry, and notoriously sent the spirit of divination out of the girl in Philippi – but not until she had annoyed him for some days. Nevertheless he and his friends did pray. Mostly for boldness and clarity in speaking about Jesus.
One question is whether Christians can be affected by evil spirits. Paul certainly thought that evil spiritual and demonic powers were strongly at work against Christians. In Ephesians (4.27) he warns the believers not to let the devil get a foothold. That is by lying, stealing, and getting angry. In Colossians (2) he thinks that believers can come under the power of the evil powers by using systems of religious rule keeping to help them become more godly.
Neither does Paul think we should take the fight to them. Our commission is to help set people free by means of the gospel. His repeated encouragement to us in the face of spiritual attack is just to stand. Stand firm. Stand against the devil's schemes. So we can keep on with the main game of making disciples.
But the devil's schemes are often subtle. They often have a lot to do with deception and lying. They often make us feel comfortable about what is wrong and uncomfortable about things that don't matter. The devil's schemes in western culture seem to be about providing sedatives, distractions and catering to our pleasure seeking, rather than any threats of violence or material loss.
And the protection? The Lord's mighty power through the gospel.
Dale