table below from ISOGG shows approximately how much Autosomal DNA is shared based on your relationship with relatives.
* The 2nd column shows centiMorgans. According to Wikipedia, a cM is "the distance between ...markers for which the ...number [representing] a single generation is 0.01." You don't have to understand this to know that the bigger the cM number, the closer the relationship.
Look at the Relationship Spreadsheet on the VincentFamily.org homepage. Compare Cousin Caroline, in Generation 2, and I (Ron.V), in Generation 3. Notice that our common ancestor is John Vincent (1787-1871) in Generation 7. His children, Aaron and Louisa are siblings. Their children are 1st Cousins, grandchildren 2nd Cousins, and so on. That makes my children and Cousin Caroline 5th Cousins. It make Caroline and I 4th Cousins, Once Removed (4C1R).
According to the above chart, Caroline and I should share no more than about 1/10th of 1% DNA, or a match of about 6 and a half centiMorgans, a very small amount. We actually match closer than that: on Chromosome 17 for 14.82 cM and Chromosome 21 for 15.13 cM. But that's because Cousin Caroline and I have two common ancestors or two common lines, the "Vincents" as well as the "Paces" (my paternal grandmother and paternal grandfather were both related to her grandfather). If you take just our Vincent ancestry and divide that number in half it's approximately equal to the expected 6.64 cM mentioned above.
This not only shows some the problems we run into by using Autosomal Matching alone. More information is needed to get the same accuracy you would with yDNA testing.