Wow, thanks to the previous posters for their superb summary of what to expect!
We haven't met our 4-yr-old daughter yet, either. We've talked with our social worker and gotten a few ideas. One thing they remind us about is that the orphanage has its own way to handle this and we may not have much say in how the first meeting is arranged.
That said, our social worker recommended taking a small, fun, shared activity--like blowing bubbles--so that you have something to do together. She sometimes takes stickers and puts them on her face, so the child will look at her (contact without the stress-the child knows what to look at). If you have sent pictures or a book, a copy of those same pictures and/or book might also be a good focus point. Sort of a way of saying "hey, I am/we are the parent(s)
you've heard about."
Please bear in mind that we haven't had a chance to try these out, but they sound like good ways to reduce the stress and make the first meeting fun.
Best wishes!