Autosomal DNA (atDNA) can be used to connect with distant cousins on any of your ancestral lines. The "reach" of this test is only about 200-250 years (from your date of birth) and so it does not go back as far as the Y-DNA or mitochondrial DNA tests. It can reliably detect about 99% of 1st and 2nd cousins, about 90% of 3rd cousins, 50% of 4th cousins, and only about 10% of 5th cousins.
It can also be used to explore your ethnic makeup or admixture.
A systematic approach to analysing your autosomal DNA matches
Step 1 – Where does the Common Ancestor sit on your tree (and your match's tree)?
Step 2 – Is the Common Ancestor obvious?
Step 3 – Generate a Shortlist of possible candidates for the Common Ancestor (by identifying and/or eliminating ancestral lines that are “unlikely” or “highly unlikely” to contain the Common Ancestor)