Re: recently bought 1971 merc 40hp....
Usually there is a lever that has a claw finger internal to the engine that wraps around something attached to the cowling normally in the back of the engine. It either pushes down on one end or pulls out on one end and in either case will move 90 degrees to open. Then the rear of the cowling lifts and the front follows in a rear end up first attitude....a bracket holds the front in place and the rear has to be up to clear it as you remove it.
Sometimes the rubber seal between the cowl and engine stick and it takes a whack with the heel of your hand.
Others have a clamp at the front and rear and the cowl comes off by lifting one side and then the other.
HTH,
Mark