As your child grows, and continues to learn about his or her unique history, it is inevitable that questions will come up - even when you least expect it. And, as a Jewish adopted child, your kid will have even more questions on the topic than other adopted kids who don't have the religion factor to deal with.
Get ready for questions like these: Was I always Jewish? How did I get to be Jewish? Is my birth mother Jewish? Is she upset that I'm Jewish and she's not? Why don't I look Jewish like the other kids in my school? How do I know if G-d want me to be Jewish? What if I don't want to be Jewish anymore? Can we have a Christmas tree like my birth siblings?
Some kids are more interested in asking about their background than others, just like some children will have a harder time establishing and finding peace with their identity than others. But everyone has questions.
-- Anticipate the questions before they are asked. My feeling - and what has truly worked for us - is to anticipate what question or questions your child will probably be throwing at you next, or what topics s/he will be looking to discuss. Even if it's not the exact question, if you have run some answers through in your head and are prepared in advance, you will be much more comfortable going through the issues with your child.
-- Don't delay answering your child. It's hard to know exactly what is going through someone else's head. Saying something like "I'll talk about this later" or "Ask me when you're older" can have devastating consequences. A child may feel less likely to approach you when something is on his/her mind if s/he feels like you are reluctant to discuss difficult topics. Only resort to pushing off the subject if you are in an inappropriate environment or there are too many distractions. In that case, say something like, "This is a great question and I want to be able to give you my full attention. How about we talk about this after our errands?"
And lastly,
-- Answer the question. Although we as parents by nature seek to protect our children from the hard truths of the world for as long as possible, I really feel that if the child is old enough to ask the question, s/he deserves an answer. That doesn't mean that you need to tell the entire story with all the details if you feel that your child is really too young to hear it all. But the answer you give should be truthful, appropriate for their age and yet should also be a satisfactory answer to their question.