There have been a slew of briefs filed in the cases (a number of separate suits were filed, and then consolidated by the Court) by both the parties and the groups acting as "friends of the court" (amici curiae). You will find links to download all of them at this page, as well as the Court's official summary, news releases, the Court's prior opinion, and much, much more.
For those wanting a quick review of the issues on both sides, as well as a realistic assessment of the arguments, this article by a civil litigator at Huffington Post does a pretty good job. (H/T: JB Chilton, at The Lead.) Over at StandFirm earlier, commenter jamesw provided links to two helpful articles about the pros and cons of the arguments in this post; later, he also provided a cite to this comprehensive analysis, which is still apposite. See also this latest post over at Volokh Conspiracy (also linked on the sidebar) for a useful summary and further links.
I will have more to say following the argument. For my thoughts as to why the entire argument about "rights" to marry is misguided, please see this post.