In the book "Knitting Brioche," author Nancy Marchant (referred to as the Queen of Brioche) writes that the earliest mentions of the brioche stitch she can find are from 1840s England. However, the brioche cushion pattern she attempts from one of those early pattern books is so incorrect she winds up with a something that looks like a cake. Pastry fans will be happy to know that Nancy's research also found that the stitch's name is a reference its spongy texture, comparable to the french bread.
When Nancy first learned how to brioche knit (in the Netherlands, where the stitch is very popular), she was taught four different ways to create the same stitch. It has both an English and Continental approach, which IKnitwithCatFur teaches here. European books also refer to the stitch as English Rib.
New Stitch a Day also goes over the basics of brioche knitting, explaining the cast on, as well as the first and second rows very slowly, along with instructions along the bottom of the screen. (You may want to enlarge the video to see them.)
Heidi Gustad of Hands Occupied explains one of the most popular derivations of the stitch: two-color brioche knitting. As Nancy explains in her book, Knitting Brioche, there are some rules to the stitch, but knitters should approach the technique with an open mind since it offers a lot of opportunity for innovation.