You probably already know this, but if you intend to hunt with it, do NOT use the surplus ammo for hunting. Full metal jacket ammo is just not good for hunting animals. Find some good commercially loaded ammo with a good soft point bullet around 180gr and you should be ready for the field.
In order to become capable, you should shoot your rifle, preferrably with the hunting ammo, at 100yds... a LOT. The more you shoot it, the more comfortable you get with it. Concentrate on consistency.... hold it against your shoulder the same way, every shot. Squeeze the trigger the same way, every shot, etc... Learn to control your breathing, to help minimize the movement due to your heartbeat (yes, you WILL have a thumping heartbeat when looking through the scope at your first deer) Learn to control it.. Hunt deer "mentally" frequently. Go through the whole scenario, mentally .... seeing the deer, getting in range, easing the safety off, lining up the crosshairs, waiting for the perfect moment, squeezing the trigger. The more you do this, mentally, the more control you will have when you actually DO it.
Your grandfather gave you a nice rifle. Do your part, think safety ALWAYS, and you should have no problems hunting deer with it.