It doesn't need an air pump, it takes a water pump. I have no experience with this particular skimmer but looking at http://www.sealifesystems.com/SeaStorm-250-Protein-Skimmer-br-with-pump.html">this site</a> it comes with a 375 gph pump factory.
Most skimmers seem to take a few days running before they stabilize. It took me awhile of tinkering with my sump and skimmer before I finally got good results. Get it in and with the pump on and see how it runs for you. Don't get discouraged, they can be picky!