To work in your core, do the pushups with the dumbells. Do a regular pushup holding onto them (so they prop you up). When you come up, as you reach the top of the pushup, pick up the left dumbell and lift it to your left shoulder (i.e. straight up), then place back on the floor and do another pushup, alternating which dumbell you pick up. It should be one continuous movement, not stop at the top and then pick up the dumbell.
The images in this article should help my poor description (and its exercises are great too):
http://www.menshealth.com/cda/articl...10cfe793cd____