Using the name of Jesus
It's true that every believer has authority to cast out evil spirits, but it's also necessary to understand the importance of using the name of Jesus when driving out unclean spirits. I heard of one evangelist who was preaching in an area where their predominate god was Mohammad, and he did a demonstration up on stage... he took a woman who clearly had an evil spirit and a man who clearly had a need for physical healing. He said to them that he's going to first try to use the name of Mohammad to cast out the spirit and heal the man, then he'll use the name of Jesus and see which one works. He tried it with the name of Mohammad, and as you can guess, nothing happened. But when he used the name of Jesus, the evil spirit departed and the man was healed!
Mark 16:17, "And these signs shall follow them that believe; In my name shall they cast out devils; they shall speak with new tongues."
Notice how Jesus makes it clear that we are to cast out the spirits using His name. Now if we look into the early church, we see Paul using Jesus' name to drive an evil spirit out of a woman:
Acts 16:18, "And this did she many days. But Paul, being grieved, turned and said to the spirit, I command thee in the name of Jesus Christ to come out of her. And he came out the same hour."
Not only did the early church drive out evil spirits with Jesus' name, but many were also healed using the name of Jesus:
Acts 4:30, "By stretching forth thine hand to heal; and that signs and wonders may be done by the name of thy holy child Jesus."
The disciples even found somebody who was not a disciple, that was using Jesus' name to cast out evil spirits:
Mark 9:38-39, "And John answered him, saying, Master, we saw one casting out devils in thy name, and he followeth not us: and we forbade him, because he followeth not us. But Jesus said, Forbid him not: for there is no man which shall do a miracle in my name, that can lightly speak evil of me."
One time I was casting some spirits out of somebody, when I commanded the spirit to look me into the eyes (they hate that), but the spirit refused even after I repeated the command a few times. Then I remembered that I wasn't using Jesus' name when issuing those commands, so I said, "In the name of Jesus, I command you to look me in the eyes!" and ZAP... here comes that head up and the thing stares me in the eyes!! There is power in the name of Jesus!