There are two types of DNA used in genetic genealogy. There is Y chromosome DNA, Y DNA, passed from father to son, and maternal DNA, mtDNA, passed from a mother to her children. A male will rarely get his father's mtDNA. So far, this has been observed one time in the past 20 years of research.
Y-DNA "For Men Only"
The Y DNA can be tested to determine a Y DNA signature for the male ancestral line of a male. The mtDNA can be tested to determine the maternal ancestry of a male or a female.
The Y DNA changes relatively rapidly when compared to the mtDNA. With the results of testing the Y DNA of several male descendants of a man with the same surname, you can determine the Y DNA signature for his male descendants and then compare other males of the same surname to him to see if they are related. Depending on how many markers are tested, 10 to more than 25, and how many differences there are between two males, none to 1 or 2, you can have a 50% chance of a most recent common ancestor, MRCA, from 400 to 1000 years ago. This means the Y DNA test can be used to focus research in a certain area if there is a match between someone with little paper documentation and someone with a fully-documented genealogy.
With a female, you would select several direct line daughters or G+granddaughters of a female ancestor and test the mtDNA to see if it matches. The mtDNA changes more slowly than the Y DNA, so it gives results on a time scale of 10,000 to several 100,000 years for the most recent common ancestor, MRCA. This result may help you determine that two people are related where you suspect the two female ancestors to be mother and daughter or full sisters. Because the mtDNA is less changeable than the Y DNA, the specificity of the relationship may be less than that determined with Y DNA testing.
The results of the Y DNA test, the markers and their scores, are called a haplotype. By classifying closely-matching Y DNA haplotypes into a haplogroup, you can get a rough idea of the ethnic origin of that particular ancestral line. The same is true, on a much longer time scale, for the mtDNA results. The mtDNA haplotype is compared to the Cambridge Reference and all differences are noted and reported to the person tested. There also are web sites for comparing your Y DNA or mtDNA results to others who have tested.
To use DNA testing to your advantage you should have a question you are trying to answer and you should choose the people to test based on the question. A broad question could be: Are the US Caperton families related to the UK Caperton families? Here you would pick several male Caperton surnamed descendants from US and UK lines and compare the results of their tests. Even within the US there are several seemingly unrelated Caperton lines. Members from these lines could test and compare their results to see if they are related.