If your hand or body is shaking pray with your hand slightly away from the person so as not to distract them. If a stronger manifestation begins to happen within you then withdraw from ministry for a while and let the Lord bless you. Laying on of hands may be appropriate, not 'leaning on of hands'. Give a light touch only, generally on forehead, top of head, shoulder, or hands. No inappropriate touching.
Some people pray aloud while they are being ministered to.
Encourage them to be quiet and just receive. It is difficult to drink in and pour out at the same time. The person you are praying for needs to be assured that he or she is the most important one for that moment. Avoid the tendency to let your mind and eyes wander to other things or other people or other situations in the room. Don't become distracted with other issues.