Boyd’s Bible Dictionary:

The weapons of shepherds and light troops
It consisted of leather or sinew strings with a pouch at the end for the missile (Judg. 20:16; 1 Sam. 17:40).

Concise Bible Dictionary:

A simple weapon with which stones were thrown. It could easily be formed of a piece of leather with a small hole in the center, and having two strings attached. A stone was placed in the hole in the leather, and swung round forcibly, when, by releasing one of the strings, the stone would fly away. It was used by shepherds to keep off such animals as wolves; David had one with which he smote Goliath. We read of some who were so skilled in its use as to throw a stone to a hair’s breadth. It is mentioned among the weapons of war (Judg. 20:16; 1 Sam. 17:40,50; 2 Kings 3:25; 2 Chron. 26:14). On the Egyptian monuments men are portrayed using the sling.

From Manners and Customs of the Bible:

1 Samuel 17:40. He took his staff in his hand, and chose him five smooth stones out of the brook, and put them in a shepherd’s bag which he had, even in a scrip; and his sling was in his hand.
1. The shepherd carries a staff which he holds in the center. It is used not only as a support in climbing hills, but for the purpose of beating bushes and low brushwood in which the flocks stray, and where snakes and other reptiles abound. It may also be used for correcting the shepherd-dogs, and keeping them in subjection. Thus Goliath says, “Am I a dog, that thou comest to me with staves?” verse 43. This useful accompaniment of shepherd life is mentioned in Genesis 32:10; Psalm 23:4; Micah 7:14, and in other passages.
The scrip was a lag of leather thrown over the shoulder, and used by shepherds and travelers to carry provision. It is still used by Eastern shepherds, and is made of the skin of a kid stripped off whole and tanned. This is the only passage in the Old Testament where it is mentioned, but reference is made to it in several places in the New Testament (Matt. 10:10; Mark 6:8; Luke 9:3; 10:4; 22:35-36).
The sling was made of leather, or of plaited work of wool, rushes, hair, or sinews. The middle part, where the stone lay, was called the cup (caph), because of its cup-like depression. It was wider than the ends, but the sling gradually narrowed toward the extremities, so that it could be easily handled. In the Egyptian sling, which probably was the same as the Hebrew, there was a loop at one end which was placed over the thumb, in order to retain the weapon when the stone was hurled and the other end became free. The sling was used by shepherds to keep the beasts of prey from the flock, and also to keep the sheep from straying. Husbandmen likewise used it to drive away birds from the fields of corn. In war it was a formidable weapon in skillful hands. The Egyptian ginger carried a bag of round stones depending from his shoulder, as David did. The Assyrians, however, according to their sculptures, had lying at their feet a heap of pebbles, which they picked up as they were needed. In using the sling, the stone was put into the broad hollowed part, the ends were grasped together in the hand, and after a few whirls around the head to give impetus, the stone was discharged, frequently with force enough to penetrate helmet or shield.
A weapon so peculiar in its formation and so great in its power was appropriately referred to as an illustration of swift and certain destruction. Thus Abigail said to David, “The souls of thine enemies, them shall he sling out, as out of the middle of a sling” (1 Sam. 25:29). Thus the Lord said to Jeremiah, “I will sling out the inhabitants of the land at this once, and will distress them” (Jer. 10:18). The figure in both these passages is drawn. not from the destructive power of the sling, but from the ease and rapidity with which, by a practiced hand, the stone was hurled from it.
The Benjamites were so skillful in the use of this weapon that some of them “could sling stones at a hair breath, and not miss” (Judg. 20:16). The youthful David showed great skill, since he hurled the pebble with such aim and force that it smote the giant in the forehead and brought him to the ground (vss. 49-50).