First, make sure you purchase them from a vendor who provides a guarantee, preferably lifetime! These pieces used to be horrible. The ultraviolet rays would destroy them in short order causing them to spilt. The formula is now supposed to include anti-crack and anti-ultra violet protections. If you bought these several years ago, you may need to think about purchasing a replacement set. Removing and reinstalling the bumpers is no picnic.
Fastening the filler strips: use the same type fasteners that were originally on the car, a hexhead sheetmetal screw possibly stainless steel, approx 1/2" to 5/8" long.