Question: "Laying on of hands - what does the Bible say?"
"Laying on of hands" is a biblical action; however, there is no biblical mandate requiring the physical laying on of hands for a particular spiritual ministry. Jesus certainly laid His hands on many of those He healed; however, He also healed without laying His hands on people. In fact, there were times when He was nowhere in the vicinity of those He healed. Matthew 8:8 describes Jesus healing the servant of the centurion without going near the centurion’s house.
Here are two instances to consider: in one case the Holy Spirit bestows the gift of speaking in tongues with the act of an apostle's laying on of hands, and in the other case He does so without the laying on of hands, but simply through the apostle's preaching.
"Paul said, ‘John's baptism was a baptism of repentance. He told the people to believe in the one coming after him, that is, in Jesus.’ On hearing this, they were baptized into the name of the Lord Jesus. When Paul placed his hands on them, the Holy Spirit came on them, and they spoke in tongues and prophesied" (Acts 19:4-6).
"While Peter was still speaking these words, the Holy Spirit came on all who heard the message. The circumcised believers who had come with Peter were astonished that the gift of the Holy Spirit had been poured out even on the Gentiles. For they heard them speaking in tongues and praising God" (Acts 10:44-46).
First Timothy 5:22 says, "Do not be hasty in the laying on of hands, and do not share in the sins of others. Keep yourself pure." The thought here is not so much in cautioning the physical action of laying on of hands but to urge care in bestowing the responsibility of spiritual leadership (however it is done). It is not to be done "suddenly" or without due consideration.
Undoubtedly, the laying on of hands in the early church was a means of connecting the message with the messenger, or the spiritual gift with the gifted giver. It provided a "sign" authenticating him through whom the physical manifestation of a spiritual gift was bestowed. We need to understand very carefully that there are no magical biblical formulas for the ministry of the church. Laying on of hands has no power in itself. Laying on of hands is only used by God when it is done in agreement with God's Word.