In my humble opinion, this is about the best thing our federal government has come up with in a long time!
We, too, were amazed that it's a CREDIT, not a deduction. In other words, its CASH MONEY that you get back (dollar for dollar, not a percentage). Next year when you do your taxes, you fill out a special "adoption tax credit" form and get credit for adoption expenses (homestudy costs, post-placement visits, agency fees, etc). The max is $10,000 per adoption (provided you make less than $150,000 a year, above this they adjust it). The adoption doesn't even need to be final, and you can carry "extra" credit over into the next year. (We had this happen because we didn't pay enough tax to take the full credit in one year. That is, if you didn't PAY $10k in taxes, you will receive back what you did pay in taxes. You can claim the rest the next year.) I think you can even claim previous expenses if the adoption isn't final.
I think this is sounding clear as MUD...sorry. If you call the IRS they can send you Publication 968 (an agency just sent this to us) and is explains some of this. Hope this helped!