Throughout the HBO show we see a variety of weddings and wedding ceremonies. My question concerns Robb Stark's wedding to Talisa Maegyr. In the show we see that they are secretly married and say the vows of the Faith of the Seven. Shouldn't Robb have been married under the sight of the Old Gods as they are the Gods of his father?

Maybe there were no Weirwoods nearby to perform the ceremony. Maybe simply being in the south is enough to mandate a wedding by septon. Maybe the Faith of Seven is a quick ceremony so Robb and Talisa can get it on sooner. Maybe there is some actual reason?

It appears as though Game of Thrones writer Bryan Cogman has already answered this one for us. Essentially they wanted to get married then and there and getting married in the light of the Seven was their best bet. He also alludes to Cat having been of the Seven and so that would play a part in it too.

Justin: Why were Robb and Talisa married in the light of the Seven rather than in front of a Heart Tree?

Bryan: Shotgun wedding! Of sorts. They wanted to get married and there was a septon readily available. At any rate, Robb was raised in an interfaith household — he could very well have spent as much time with with Septon Chayle growing up as he did in the godswood. So I don’t see a problem with him having a Seven wedding. But I guess a lot of people do cuz I get asked that question all the time.

Now the line about Karstark praying to the Father in 208… yeah, I should’ve caught that. Karstark would be strictly Old Gods, I think. If it helps, you could read it as “I’d even break my faith and pray to the bloody FATHER if that’s what it took to bring my sons back”… but I’m not sure that was the intent. But maybe it was. I try my best!

_{Winter is Coming, Ask a GoT Writer: Bryan Cogman on the writing process, Robb and Talisa, and Renly’s peach}

There is not much information on how the wedding was performed in the books:

"I took her castle and she took my heart." Robb smiled. "The Crag was weakly garrisoned, so we took it by storm one night. Black Walder and the Smalljon led scaling parties over the walls, while I broke the main gate with a ram. I took an arrow in the arm just before Ser Rolph yielded us the castle. It seemed nothing at first, but it festered. Jeyne had me taken to her own bed, and she nursed me until the fever passed. And she was with me when the Greatjon brought me the news of . . . of Winterfell. Bran and Rickon." He seemed to have trouble saying his brothers' names. "That night, she . . . she comforted me, Mother."

Catelyn did not need to be told what sort of comfort Jeyne Westerling had offered her son. "And you wed her the next day."

He looked her in the eyes, proud and miserable all at once. "It was the only honorable thing to do. She's gentle and sweet, Mother, she will make me a good wife."
_{Catelyn II, a Storm of Swords}

Not much more than that is said about it. The same information as @TheLethalCarrot gives still stands, there are not many Weirdwoods in the south, so most likely they grabbed the first septon they could find and rolled with it.

Another thing to note is that Jeyne Westerling, opposed to Talisa was from the Seven Kingdoms, and holds to the faith of the seven. So it makes more sense since they were both brought up (partially) with that faith.

Jeyne vs Talisa

This is one of the few subtle (ahem) differences between the show and the books. The writers of the show reportedly changed the character Jeyne so much that George R.R. Martin requested them to change her name, to avoid confusion:

57 minutes: He talked about how he suggested that the name of the character Robb married in Season 2 be changed to Talisa, given that this was an entirely new character that book readers would not be familiar with (in the novels, Robb's love interest has a different name and history).
_{'Game of Thrones' Season 3 Characters And Scoop From Creator George R.R. Martin}