The most common thing parents do is try to (force) a change on their children instead of meeting them where they are personality wise.
Parents need to listen to what makes their child tick, their likes and dislikes, along with their fears. Knowing where they are coming from helps a parent to gradually show them that confidence comes from succeeding at little things and eventually succeeding at bigger things.
Lastly it's important to let a child know you love them period. Not everyone has to be an extrovert, the life of the party, social butterfly, or class clown. The goal in life is to be comfortable in your own skin!
Know yourself, Love yourself, and Trust yourself.
Yelling at a child, forcing him/her to join clubs/leagues they don't want to join, or berating them because they are "not like" another child sends them a message that you don't love them for who (they) are.
When children feel unloved and disconnected from the people who brought them into world it's a very lonely place for them. A person's personality has to (evolve) overtime with their own doing.
Maybe the best thing a parent can do for an introverted child is have them participate in activities that do not require a group of other people such as taking private piano/music lessons, or studying something that so interest them that they could careless who else is in the room like magic tricks. Focus on whatever excites them!
If a parent can find out (what the child loves to do) and support them in developing that skill it will go a long way to increasing their confidence and self-esteem. When you know you're "good at something" your life changes for the better.