The Guild of One-name Studies, of which I am a member, held a seminar on "DNA and Genealogy" last year at the Ashmolean Museum in Oxford.  It was really stimulating and has encouraged me to try and start a DNA project of our own. 

The theory: 

• The Y-chromosone, a tiny component in our genetic make up, changes the sex at conception of those of us who go on to be born male.
• By taking advantage of recent steps in genetic science, markers from the Y-chromosone can help identify a connection between people who have a common male ancestor through paternal lines
• The Y-chromosone is passed from father to son intact and more-or-less identical
• Since surnames in our culture follow the male line, Y-chomosone testing of people with the same surname can establish the probability of their having the same common ancestor 

• the probablility that they have the same common ancestor
• the probability that variant surnames are genetically linked
• the probablility that there is just one male common ancestor at the head of our one-name study, or if, in fact, it is more probable that there are several distinct points of origin on the male line

• Our DNA Project 

• DNA Heritage’s Tutorial  (which has been written especially for non-scientists.) 
• DNA Heritage's  FAQ page