YOu can use a clean rag, but if you absolutely want to make sure you are not putting lint in the finish, then wash your hands very well, and then apply the tung oil thinly with your fingers. Stretch the oil to cover as much area as you can, before dipping a finger in the can for more oil. Only a few drops will be needed to coat the stock each time. You want to do many coats, polishing each coat after it dries with a coarse cloth, building layers of finish until all the pores are filled, and you get the kind of surface finish you are looking for.
If you want the final finish to be matte, rather than shiny, put the finish on with your fingers, as with prior coats, then 5 minutes later, come back, and using very clean hands, run your fingers gently over the surface of the finish to break up the sheen. You will be left with a satin, " Matte " finish that has less flash to it. When it dried, rub the stock down with burlap, which will further dull the sheen and give your stock that old time look. The nice thing about tung oil is that if you do get a scratch to the finish, you can repair it easily with just a small drop of tung oil rubbed into the scratch and then blended into the surrounding surface.
