I tried two ways of holding a pencil. The first way is the normal way, which is where you hold the pencil between your thumb, first finger and second finger. This is sometimes called the tripod grip. The second way is where you hold the pencil between your thumb and first finger with the pencil resting over your palm. This is sometimes called the claw grip. I tried drawing circles with these grips first on an easel then in my sketch book.
I think that the tripod grip is better for small drawings or intricate detail but the claw grip is better for bigger, more free movements.