The brp (brioche purl) stitch is always worked together in combination with a slyo (slip and yarn over), and they combine with the brk (brioche knit) stitch, to create the typical brioche fabric together.
Brp: On the purl column, purl the stitch together with its corresponding yarn over. When you are working this in a contrast colour, the yarn over will be the main colour, and the previous stitch the contrast colour.
Slyo: Bring the yarn forward in between the two needles. Slip the next stitch (which is a knit stitch) from left to right needle as if you are purling it, and bring the working yarn back forward between the two needles to work the next purl stitch. You have now added a yarn over in the contrast colour to the knit stitch in the main colour.