How can I help my child overcome shyness?

Patience. Babies transition thru stages in life. Under 6mo they may be interested & happy with everyone, then go thru an awakening to realize how much they depend on you. This results in separation anxiety, a normal finding. It varies with child & situation & may continue for some time. They grow up understanding you, but not new people, settings, etc. Work with them to enjoy such events & this should pass.
Take it slow. First, realize that "shyness" may just be a normal part of your child's temperament. It may take him/her longer to get used to new situations or people or changes in routine. It is not necessarily something which needs to be "overcome". But, in general, prepare your child for new situations, practice what to say and do when you meet new people. Overall, be patient and accepting.

Related Questions

How can I help my child to overcome her shyness?

Make her feel safe. Kids are normally shy when they are young. You do not mention your child´s age, but being shy is part of a personality trait and not a disease. Most people, adults and children alike feel shy" when they around strangers or large gatherings, not to mention when they have to give a presentation at school. Let her know it is ok to be shy and avoid pushing her. She will blossom when it is right.