Calmness can most easily occur for the average person during a state of relaxation, but it can also be found during much more alert and aware states. Some people find that focusing the mind on something external, or even internal, such as the breathing, can itself be very calming.
Calmness is a quality that can be cultivated and increased with practice. It usually takes a trained mind to stay calm in the face of a great deal of different stimulation, and possible distractions, especially emotional ones. The negative emotions are the greatest challenge to someone who is attempting to cultivate a calm mind.