First catch your polar bear, which you do by darting it. Occasionally this results in the bear stopping breathing (I think they've done further studies on the various drugs since so this is less of a problem these days).

Once you have established that your bear is definitely not breathing, lay it on its side. Seize the loose skin over the ribcage and heave upwards. Then let go. This allows you to work the lungs like a bellows. Continue until your arms drop off or the bear starts breathing again on its own. Run for the helicopter.