Originally Posted by Thorpesaurous
It's actually Stannis' wife who innitially turns to the R'hollor, the god of light, and he winds up being lured over to it. They don't explicitly say that he's lured to it by the "clear the table and get it on" sexual approach of Melisandre, but it is somewhat implied. I also don't recall specifically if it's because of this, but I think it's also implied that it's due to her seeking resolution for their ill daughter, neither of whom we've met yet. And the fact that she worships Stannis nearly as much as she does her red god may have something to do with his conversion.
Stannises daughter was sadly not written for the show. Great summary btw.