Wear disposable protective gloves. Hold the grip in your hands while you liberally apply the tung oil. Wait five minutes, then remove ALL the excess tung oil with paper towels. Place the grip in a warm place to allow the oil to cure/oxygen polymerize, for at least 48 hours. Soak the paper towels in water for 24 hours, then dispose (extremely important to prevent a fire!).
By the way, tung oil is not superior to any other finish EXCEPT that it won't radically change the original color of the wood. Otherwise, there are many other finishes which are superior, including "Min-Wax rub-on finish", which I used for 15 years in my furniture company, before retiring. Tung oil has an undeserved reputation for durability (at least compared to modern finishes). It is very easy to repair after damage, however.