Yes, the spider plant is one of the easiest plants to propagate. If you look closely at the babies, or plantlets, you'll see some little knobs on the underside of the cluster of leaves. Those are root initials. If you place them on potting soil, the roots will start to grow, and you'll have new plants.
If you like, you can leave the plantlets attached to the mother plant until they form roots, or you can cut the plantlets off the mother plant and put them in separate pots. Just be sure to keep the soil evenly moist until the roots are fully developed. In no time, you can have enough spider plants to share with friends and neighbors.