Direct to paper means the ink is applied to the paper right from the ink pad. You either drag the card edges through the pad or rub the pad lightly onto the card.
I just did one for a challenge so I'll linked it and I did both rubbing the pad over the card and then just the edges through the pad. The sharper sort of pointed marks was achieved by rubbing just the corner of the pad over the card.
Bear Card
I didn't have any purple cardstock when I did this card so I just rubbed white textured cardstock through the ink pad and came up with what you see in the dark purple border. With it being textured it come out with white still showing.
Flower card
I hope this answers you.