If my brother hit a cow that was in the middle of the road, how do we go about getting compensation from the owner of the cow?

It's not a police matter--the police only deal with criminal matters, and a wandering cow is not a crime.

If you believe the cow's owner was at fault--was careless in letting his cow get out into the road, whcih is likely the case--you would begin by submitting a claim or demand for payment to him. He or his insurer may choose to pay...but if they don't, then you'd have to sue him (his insurer, if any, would step in to defend the case) and prove in court that he was negligent, that your brother was not (since his negligence would reduce what he could receive as compensation), and also the extent of the damages (such as the cost to repair the car).