All you want to do when cooking fresh tuna is to sear both sides of the steaks on high heat for 3 - 4 minutes. While the outer sides of the tuna should be browned, the inside of the tuna steaks should be pink or red. You'll know that you've overcooked the tuna if the inside turns a dull grey color - at that point, it's going to be dry and unpleasant to eat as is.