I would first clean and vacume the flooring and then install the pad.
Then I would install the strips all around the perimeter, cutting away some of the pad to allow for this strip.
Attaching the strip to the cememt could be your biggest challenge.
Carpet strips have attached or started concrete tacks that in most cases work, but on old set up concrete, sometimes they just bend over.
The key to installing the tacks strip is to hit each nail with ONE direct blow and never hit it again. The second blow only loosens the fit. If this does not work, consider the tapcon nails, or even the Remington 22 nail driver. Tapcon may work, if not the Rem 22 will definately do the job, use the light load though.