[header] How to respond after hitting a dog or cat with your car [title] Pull off to the side of the road immediately. [step] Slowly drive or coast your car to the shoulder of the road. If you were in a lane near a median when you struck the animal, then you might need to pull onto a soft patch on the median. 
Make sure you are completely out of any lanes of traffic, but relatively close to the pet you hit. [substeps] Ideally, you won't have to cross the road to reach the stricken animal.