Genetic genealogy can be confusing, so let me see if I can break it down and simplify it for you.
Everyone gets half of their DNA from their mother, and half of their DNA from their father. Following that, grandchildren get about 25% of their DNA from each grandparent. Each generation further back contributes 50% less. So:
50% from parents
25% from grandparents
12.5% from great-grandparents
6.25% from great-great-grandparents, etc.
You'll also share certain amounts of DNA with living relatives. These average amounts can be used to predict relationships between two people.
50% with full siblings
25% with grandfathers, grandmothers, aunts, uncles, half-siblings, double first cousins
12.5% with great-grandparents, first cousins, great-uncles, great-aunts, half-aunts/uncles, half-nephews/nieces
Here is a picture of the DNA that I share with my father (green), my mother (blue), and my maternal grandmother (purple). As you can see, the green and blue lines cover all my genes, and the purple one has some breaks in it. This is because each of my parents contributed 50% of my DNA, but I received only 23.3% of my DNA from my maternal grandmother.
By comparing DNA with people, you can confirm how you are related to someone, or figure out how you are related to someone based on how much and where they share with you. By testing known relatives who are more and more distantly related to you (ie, parents, cousins, grandparents, second cousins, etc), you can begin to see where certain segments of your DNA came from. This can lead to helping adoptees find their birth families, or finding common ancestors with other people you share DNA with.
Just for grins and giggles, here's the same picture as above, with my maternal grandfather's first cousin (orange) thrown in. Our common ancestors are my great-great-grandparents Johann Loewen and Katharina Epp. As you can see, for the most part, purple (my maternal grandmother) and orange (maternal grandfather's first cousin) do NOT overlap. This is because one is from my mother's maternal side (purple) and one is from my mother's paternal side (orange). There is one small segment on chromosome 3 though, that does overlap, which indicates that somewhere back in the family tree, my maternal grandmother and my maternal grandfather's first cousin share a common ancestor.
Do you have any questions so far? (Note: I am planning to add some fancy graphics to this post to demonstrate DNA segments.)
