How can someone be a quiet person depends on what is going on inside them?
Sometimes immense grief and inability to express something makes a person quiet. In this case they are not able to share their feelings with someone else, thus, instead of lamenting they find being quiet a better option.
In other case, people who are truly blissed within themselves and are smart enough to understand not every situation requires a reaction, they prefer to remain quiet mostly; not because they don’t have enough things to say but because they prefer quietness and calmness more relaxing.
As understood these are two totally contradicting cases.
If someone wants to become quiet by a choice he/she should practice spending some time alone in solitude- just engage themselves in making observations. They could first observe their thoughts and emotions and later observe their surroundings. Being able to remain quiet and self-sufficient is a great quality and nothing to be ashamed of. A person who is quieter is a great observer.