To see yourself shaking hands with a prominent figure in a dream is a good omen and foretells prosperity, success, rapid climbing of the social and career ladder, increasing gains etc.
Shaking hands with people you know or with strangers in a dream usually bears a positive significance and is reflective of your friendly nature. You are a people's person, clubby, natural, free and easy. Also, you are ready to lend a helping hand to those in need and offer unconditioned support to people you care for. This is why shaking hands as dream image may stand for the admiration and gratitude the others show you in the waking life.
On the other hand, shaking hands and taking someone for a true friend may be tricky sometimes - those whom you consider open and trustworthy friends may prove to be sly and hypocrite individuals willing to take advantage of you and use you to achieve their own goals. Therefore, pay attention to whom you confide in the waking life, as you never know...