Once you have your clusters, there are many directions to look at for further research.

Start with what you know

You probably already know how some of your matches are related to you. Find the clusters that contain those known relatives, and start from there. If you have a fourth cousin who is related to you via one particular pair of 3rd-great-grandparents, the other members of the cluster might also be related through those same 3rd-great-grandparents. Or the other cluster members could be related through one of the descendants or ancestors of those 3rd-great-grandparents. See if you can find anything that looks familiar in the public trees of the members of the cluster.

Public trees

Public trees, both linked and unlinked, can be a great source of easy information. Looks at the trees for names that you recognize. Look for names that you don't recognize, but which appear in several trees. Look for geographical locations that show up in several trees.

Remember that while all members of a cluster likely share the same DNA segment, that does not mean that they all necessarily share the same common ancestors. A cluster could contain a mix of second cousins, fourth cousins, sixth cousins, etc. If a tree has some familiar names or locations, try creating a quick and dirty tree to see if you can extend the tree earlier in time to find ancestors that are in your tree already.

Send messages to the matches

You might not know how all of the members of a cluster are related to each other... but that doesn't say what they know. So ask!

You can send messages to the members of a cluster and ask if they know anyone else in the cluster. This should be useful information to them. All of the people in the cluster are likely related to them, too.

Some people won't respond. Some will respond, and tell you that the cluster includes some of their close relatives (parents, children, etc) and they don't know anything beyond that.

If you get lucky, you can find someone who knows a lot about their own history, and is willing to share.