I have installed several half walls in homes I have owned. If the wall runs perpendicular to the floor joists just screw it through the subfloor into each joist. If it runs parallel, then you need to bolt through the floor plate and subfloor every couple of feet and use either a piece of 2x4 or 3/4" plywood as a washer under the floor. Unless it lines up right on top of the joist. The trick is attaching the plate solidly to the floor. Toenail each stud to the plate from all four sides. The wall should feel pretty sturdy at this point. Once the drywall is on it ties it all together.