Is there a word that describes how a person grabs a pencil or a paper with his index-finger and thumb?
As the comments indicate, hold is the most appropriate verb when not describing the use of just the index finger and thumb.
The synonyms for hold which @Mari-LouA provided can be of use, but only when you describe the way the person is clasping, clutching, grasping, gripping, clenching, or clinging to the pencil, pen or paper. For example, "He gripped the pencil between his index finger and thumb."
Using the synonyms without the description of using the index finger and thumb would generally indicate the use of more digits or even the whole hand.