Mark, two common ways are 1. shooting nails through into the concrete. 2. setting the plate in a generous amount of construction adhesive. Since none of these are bearing walls, I like the adhesive method.
Hi Mark: I prefer to drill a hole, use a lead anchor and anchor the 2X4 to the concrete floor, using a 2 1/2″ X 10 screw. I put these down every 6 feet or so. This way, the bottom of the wall will never kick out….even a little bit.