Back when the Wings West kits were all the rage, they used a combination of self-tapping screws and a foam-based double-sided tape.

Screws were used on the bottom side of the side skirts and underneath the front bumper; the tape was used to hold the top edge of the kit fast against the OEM bumper moldings.

While I'm generally not a fan of any body kit, it would help if you can link us to the kit you've bought. The correct solution depends heavily on the kind of kit and the material it is made from.