Step One - Identify all the ancestors for yourself that you can. (like Ancestors of Kristina Hewitt) Consider listing them somewhere you can share. Try to aim for at least all 32 of your great great great grandparents. True 4th cousins will share a great great great grandparent.
Step Two - Contact all your matches. It is impossible to tell which will be key matches that will reveal new information. Chances are good that most of your matches are indeed cousins. Invite everyone to share that is on your DNA relatives list.
Step Three - As each DNA relative accepts your invitation to share, compare their DNA to yours, using Advanced Family Inheritance under Ancestry Tools.
Step Four - Enter each match into a spreadsheet. You could also use 529andYou if you use Chrome, in fact I recommend it highly, but I also use a spreadsheet so I can add custom notes. You will need columns for the matches name, the chromosome that has a matching segment, the start of the segment, the end of the segment. I also like to include the size of the segment match in cM. You can also use DNAgedcom.com to download your matching segments for you.
Step Five - Identify all the ancestors for your match that you can. This is time consuming. Insanely time consuming. Even if they give you the info for all 4 of their grandparents, you will need to find/verify their 8 great grandparents, 16 great great grandparents and 32 great great grandparents. Thats 8+16+32=56 people. And that is if they are actually true 4th cousins. I've been experimenting with various methods to try to make this less time consuming. I've been playing with Geni, WikiTree, and FamilySearch FamilyTree. We really need a shared tree to start to make large steps forward in finding matches.
Step Six - Identify if there are any known common ancestors between you and your match. This is perhaps the trickiest part. It is possible that a common ancestor is not the source of the matching DNA segment. It is very common to have many common ancestors with a person. The more people in who match each other in a segment and also have the same common ancestor, the more likely that that is the ancestor who is the sources of the matching segments. Also, segments from closer relationships (4th cousins and closer) are more likely to be from the suspected common ancestor as there are less possibilities with equal probabilities.