Approximately 6 months after their first steps, most toddlers adopt a much more mature walking style, keeping their feet closer together and moving more smoothly. With support, many are now capable of walking up and down stairs. If alone, however, toddlers are still at risk for falling down stairs, so safety gates blocking off unsupervised stairways are recommended.
References
Shelov, S. P. (Editor-in-Chief). (2004). Caring for Your Baby and Young Child: Birth to Age 5. The American Association of Pediatrics. Revised edition. New York: Bantam Books.