Paternal lineage is determined by reading the Y-Chromozome. The Y-Chromozome is passed only through the male line, and only from father to son. Only men possess the Y-Choromosome. In order to determine a female's paternal lineage, it is necessary to obtain a DNA sample from a male relative
"As with maternal genealogies defined by mtDNA, men tend to cluster into a small number of groups, 18 in total, which can be defined by the genetic fingerprints of their yDNA. In native Europeans, for example, there are 5 such groups, among Native Americans there are 4, among Japanese people there are 5, and so on. The men within each of these groups are all ultimately descended from just one man, their clan father. Obviously, these ancestral clan fathers were not the only men around at the time, but they were the only ones to have direct male descendants living today. The other men around, or their descendants, had either no children at all or only daughters. These clan fathers also had male ancestral lines and these ultimately converge on the common paternal ancestor of every man alive today. This man, known as “Y-Chromosome Adam”, lived in Africa 60,000 – 80,000 years ago."
The service provided by Oxford Ancestors, of course, isn't free. The basic service costs £180 ($419.00 CDN)