According to the book, [since this is in the book section] Arwen and Aragorn were married on Midsummer, which would have been about 2 months after the crowning of King Elessar on 1 May [by the Shire reckoning].
As for what their wedding would have been like one can only guess based on what they have read. A traditional Elvish betrothal and wedding [according to "Morgoth's Ring"] would have gone as thus-
Quote: In due time the betrothal was announced at a meeting of the two houses concerned, and the betrothed gave silver rings one to another. According to the laws of the Eldar this betrothal was bound then to stand for one year at least, and it often stood for longer. During this time it could be revoked by a public return of the rings, the rings then being molten and not again used for a betrothal.
Whether this happened between Aragorn and Arwen, I can not say. Continuing on-
Quote: After the betrothal it was the part of the betrothed to appoint the time of their wedding, when at least one year had passed. Then at a feast, again shared by the two houses, the marriage was celebrated. At the end of the feast the betrothed stood forth, and the mother of the bride and the father of the bridegroom joined the hands of the pair and blessed them. For this blessing there was a solemn form, but no mortal has heard it; though the Eldar say that Varda was named in witness by the mother and Manwë by the father; and moreover that the name of Eru was spoken. The betrothed then recieved back one from the other their silver rings; but they gave in exchange slender rings of gold, which were worn upon the index of the right hand.
If there had been an Elvish wedding, I believe Galadriel would have stood in for Arwen's mother, and Elrond for Aragorn's father. Anyhoo-
Quote: Among the Noldor also it was a custom that the bride's mother should give to the bridegroom a jewel upon a chain or collar; and the bridegroom's father should give a like gift to the bride. These gifts were sometimes given before the feast.
Besides these things, it was the act of bodily union that achieved marriage, and after which the indissoluble bond was complete.
 I think we all know what that means without an explanation.
All that info comes from the book "Morgoth's Ring" a companion novel to the Silmarillion. It's a really good read, and really goes into detail about the customs of the Elves.
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...lol
I've never seen those before though, and I'm annoyed with myself that I let some Tolkien books slip through my fingers!! Ah well, now I'm really excited to read them.