For a good overview of the decision itself and the legal impact, visit our friend's blog over at Finn & Eaton: Obergefell v. Hodges: Supreme Court Rules on Same-Sex Marriage, Part 2.
For now we're posting the tl;dr version of the majority and dissenting opinions:
Here is what each opinion seems to say about the author's view of marriage:
Robert's Dissent: Marriage is an institution.
Scalia's Dissent: Marriage limits your expression.
Thomas's Dissent: Marriage has nothing to do with liberty.
Alito's Dissent: Marriage is for procreation.
Kennedy's Majority Opinion: All you need is love.
Below is a slightly more in depth analysis:
Majority Opinion written by Justice Kennedy and joined by Ginsburg, Breyer, Sotomayor and Kagan
tl;dr: Marriage is a fundamental right under 14th amendment due process and extends to same-sex couples because there is no rationale to deny benefits based on the societal reasons for promoting marriage. This was not based on a typical equal protection analysis, but rather focused on the nature of marriage and why it's important in today's society and therefore represents an inalienable liberty.
Justice Roberts' dissent joined by Scalia and Thomas
tl;dr: Extending due process rights to marriage = judicial law-making because the history of marriage is clear and the legislative process was doing just fine. Criticizes the majority for ignoring typical equal protection analysis.
Justice Scalia's dissent joined by Thomas
tl;dr: Scalia really wants you to know that he agrees with Roberts but wants to drop the pretense that he "respectfully dissents". Also, Californians aren't real westerners and hippies have more fun (seriously, he said that).