How to bring up a shy 2.5 years old girl?

vet

Simply bring her out more often. Playground, shopping, relatives or your friends gathering. Let her meet different people. Encourage her to talk to strangers such as saying thank you to bus driver, taxi driver or anyone. At the same time, you yourself have to talk as well. If she sees you talk to strangers or being socialable. She will follow eventually. Don't worry too much.

vet

Don't force her to say "Hi" to people at the begining. If she refuses, ask her why afterwards and explain. If she does, praise her afterwards. But yourself will have to say "Hi" to people, she will learn from you.