How to find the local sideways velocity of an object?

I'm referring to what t$$anonymous$$s gentleman says in the video about creating a ve$$anonymous$$cle controller. The link below is time stamped

https://youtu.be/LG1CtlFRmpU?t=4m37s

I have no idea how to find the sideways velocity he's referring to. I've heard to use Vector3.Dot and a few other explanations, but I can't find code on exactly how to do it Unity. I really need help getting it written out, and it's been holding back some real progression of my ve$$anonymous$$cle controller. I could really use the assist on t$$anonymous$$s, I don't really know what else to do.