Nice to Meet You!

My daughter, who tends to be on the shy side, was having trouble speaking to people when introduced or when prompted. I don't mean talking to strangers. I mean the people you'll encounter more regularly (at church, neighbors, family that comes to visit every few months, etc). At 2 I don't expect her to carry on a full conversation, but we are teaching her to say hello and answer brief questions (How are you _____? I like your dress! Aren't your sparkly shoes pretty!!) when asked.
So we tried playing what I call the Nice to Meet You game.
Materials: dress up clothes (any will do!)

Activity: I dressed up and tell her that we are at church/store/etc and she's will her mommy. I then say hello and compliment her. The conversation goes something like this:
Elderly lady at church: Hello! How are you this morning?
Daughter: Good! How are you?
Lady: Fine, thank you. I like your pretty dress!
Daughter: Thank you!

Then I change clothes, and we try it again! It's that simple! Sometimes I close her door to her room and knock, or we use her grocery cart and pretend we're at church. We've talked about how when someone says "I like your ____" it's a compliment and she's to say thank you.

For older children, this is a good way to role play encounters with strangers/semi-strangers. It's a good time to talk about a code word for your family and things to do and never to do.
At 2 we haven't gone there yet because of lack of understanding. At her age, however, she is not out of my sight except when I specifically drop her off at her Sunday school class with her teacher. For your particular situation, be aware of the situations your child will be in and use your discernment.