Same sex couples in every state of the country can marry.
You can find the decision here:
Same sex couples in every state of the country can marry–something many in our country never expected. And it brings about a change many older gays and lesbians never dreamed possible. (The  decision was a close one–a five/four vote by the nine Supreme Court Justices. But even a five/four decision by the Supreme Court is still the law of the land.)  As Vice-President Joe Biden might say, “it’s a big f…… deal.”
Further, if they (a same sex couple) were already married anywhere that allowed such a marriage, and moved elsewhere, the state they moved to may not deny the validity of their marriage.   (All prior state laws or state constitutional provision trashing such marriages or denying recognition of such marriages, has been deemed unconstitutional by the U.S. Supreme Court 6/26/2015.)
The case, of course, also has a Michigan connection since the DeBoer et al. v. Snyder, Governor of Michigan case–first heard in front of Michigan Federal District Judge Bernard Friedman, was consolidated with the Obergefell case and one other.  (By the way, Judge Friedman will marry the Michigan couple, according to this report:
Under Michigan law, in many many areas, such as estate distribution, determination of next-of-kin, divorce law, adoption law, pension benefits, and scores of others, the term spouse is used, and sometimes even the term “husband” or “wife” is used.  Lots of Michigan court forms will need revision now.  The Michigan Treasury will need to approach same sex married tax returns differently than they have in the past.  A gay married couple should now be able to hold property in a form known as tenancy by the entirety.
Some of these changes will happen more or less automatically, but others will require action by same sex couples in Michigan.  If you are part of this group make sure to take all the steps necessary to protect yourself.
Here is just the  tail end of the majority decision authored by Justice Kennedy of United State Supreme Court:
. . . The Court, in this decision, holds same-sex couples may exercise the fundamental right to marry in all States. It follows that the Court also must hold—and it now does hold—that there is no lawful basis for a State to refuse to recognize a lawful same-sex marriage performed in another State on the ground of its same-sex character. * * * No union is more profound than marriage, for it embodies the highest ideals of love, fidelity, devotion, sacrifice, and family. In forming a marital union, two people become something greater than once they were. As some of the petitioners in these cases demonstrate, marriage embodies a love that may endure even past death. It would misunderstand these men and women to say they disrespect the idea of marriage. Their plea is that they do respect it, respect it so deeply that they seek to find its fulfillment for themselves. Their hope is not to be condemned to live in loneliness, excluded from one of civilization’s oldest institutions. They ask for equal dignity in the eyes of the law. The Constitution grants them that right. The judgment of the Court of Appeals for the Sixth Circuit is reversed. . .