But which one should you really pay attention to! It seems like you are getting thousands at once at times! Most have 12-marker matches, or 24-marker matches. But the ones you want to watch for are those where you are most likely to have a common ancestor within 3-4 generations, and the ones you are most likely have that close of a relationship to will be 60-marker matches. Once you go past the 3rd or 4th cousin line, you will find it harder and harder to make a match.
First, contact the person if they have not listed their family tree for perusal. Ask if you can get just a straight lineage for their ancestors (parents, grandparents, gr-grandparents, gr-gr-grandparents, etc.). If something matches after about the gr-grandparents or gr-gr-grandparents, you build on it from there and begin sharing information with one another.
Family Tree Magazine's blog had a great article a couple of years back. Here is a portion of their advice:
"If you’ve taken an autosomal DNA test at 23andMe, AncestryDNA, or Family Tree DNA, you likely have a long list of genetic cousins. After sequencing portions of your DNA, the testing company compares your results to the results of other test-takers in its database. If you share enough DNA with another test-taker in the database, you’ll see that person in your list of matches.
Or from 23andMe HERE: