The Biblical method for casting out demons would be to pray as the Holy Spirit directs. Usually this would be a prayer similar to this: "In the name of Jesus, I cast you unclean spirits out of this person." Should the Holy Spirit give you specific names of demons, these most generally would be for the benefit of the person who is receiving the deliverance as they may need to be aware of the nature of the demon that has held them in bondage, so as to resist him in the future (For instance, a demon of lust or anger).
The most important thing is to listen to the Holy Spirit's direction regarding individual cases. Faith is the key to getting people free of demons. We must have faith when we pray that the demons will leave. If we believe they will leave instantly, then that will happen; if we believe we are in for a real battle, then we will end up fighting it out with the devil. Or we can even lose the battle if we don't stand firm in our faith and trust in Jesus. Some deliverance does require a prayer battle as little or no intercession as been previously done for the person bound.
Jesus' disciples had a problem with not being able to cast out a demon from a child because they lacked faith. When they asked Jesus why they couldn't do it, He answered in Mark 9:19, 23, 26, 28 -29 : "He answereth him, and saith, O faithless generation, how long shall I be with you? how long shall I suffer you? bring him unto me....Jesus said unto him, If thou canst believe, all things are possible to him that believeth....And the spirit cried, and rent him sore, and came out of him...And when he was come into the house, his disciples asked him privately, Why could not we cast him out?
And he said unto them, This kind can come forth by nothing, but by prayer and fasting." The message Jesus was trying to get across to his disciples was that their faith was not sufficient for the job, and that the way their faith would be increased was by fasting and praying. He didn't mean for them to go fast and pray to get the demons out. Jesus was immediately able to cast them out because He was always praying, and He stayed close to the Father, thereby having faith and power over the devil at all times.
Jesus is our example. If we are not in close communion with the Father, how will we be able to hear His instructions when discerning and praying for deliverance? We need to fast and pray if we find our faith and closeness with God being attacked, then we will be able to exercise our faith when praying for others and see them set free in the name of Jesus.