A few years ago I had the priviledge to meet and have a chat with Terry O'Neill who has done portraits of everyone from Sinatra to Simon Cowell. He gave me some advice which has really helped me in this regard.
Don't fill your photographs with unrelated clutter which distracts from the subject. Instead find out a little about them in advance. Give them a call or meet them beforehand to talk about the things which are important to them. It might be a hobby, a specific location or an object. Then surround them with those objects or concepts when doing the portrait and you will see their personality shine through during the shoot. They will be comfortable enough to show you a little of themselves.