To shoot and kill a deer with a Mossberg 500 shotgun, one must first find a suitable hunting location where deer are present and shots can be clearly made. Next, locate a deer by looking for signs like scraped tree bark indicating their presence. Once a deer is in sight, get into a comfortable shooting position and aim through the crosshairs, targeting behind the front leg where vital organs are located. Finally, pull the trigger, then track the deer using the blood trail left to find and retrieve the kill.