I've been involved in deliverance ministry. Our team would endeavor to follow the following process:
Interview
Confirmation
Deliverance
The interview consisted of listening to someone's request to have deliverance from an evil spirit. They'd be asked about any demonic manifestations, experiences, dreams, occult involvement, addictions, and hidden sin. If liberty was felt in the Spirit we'd endeavor to serve them. We'd focus on deliverance with regards to individuals and locations such as homes or apartments.
The confirmation involved a process wherein we'd spend an evening with the petitioner. We'd set the tone of prayer, worship, and Bible study. We'd turn off most electrical lights, accept for the room wherein we were fellowshipping. We'd anoint doors and windows with oil. We'd also anoint the individual with oil. We'd worship and lift up Jesus as we walked through the home or as we fellowshipped the individual. Normally, if a demonic spirit is present it makes itself known through "manifestation". This could be a sudden change of behavior in the individual, strange sounds, objects moving of their own accord such as doors shutting, pictures falling off of walls, etc. Manifestation could also be strange unidentifiable sounds such as voices, footsteps, screams, animal noises, creaking etc. Once we had a manifestation... we shifted into deliverance.
The deliverance typically consisted of laying hands on the individual in question should they be the target of demonization. Open rebuke would then be performed, sometimes with reading various passages of the Bible relating to spiritual warfare. We'd continue the deliverance cession until the individual returned to normal or the home settled and the peace of God came to rest in the situation.
Yes, there was more detail to a lot of this. But it really wasn't all that complicated.