Karen pretty much hit it on the head. The other thing to remember is whether or not you employer reimburses you. If you had $15,000 of allowable adoptions expense and your employer reimbursed you for $10,000, then you would only be eligible for $5,000 of the credit.
Also, you can only take the adoption credit in the year that the adoption is finalized if you are adopting from China. My wife and I started our adoption in March of 2005 and brought our daughter home in December of 2006. So, we can take the adoption credit when we file our 2006 taxes. If we had been a month later, we would have had to wait until we filed our 2007 taxes (march of 2008) to claim the credit. People who adopt domestically can take it in the year they start the adoption.
According to my tax guide, the adoption credit for 2006 is $10,960 and for 2007 is $11,390. Phase out for 2006 starts at $164,410 and totally disappears at $204,410. If you do not use the full credit this year (your liability was less than $10,960), you can carry it foward for up to 5 years.
"Taxpayers who adopt a child with special needs are allowed to claim the full amount of the credit regardless of actual expenses paid or incurred in the year the adoption becomes final."
Also, married couples must file a joint return in order to claim the credt. The link to the instructions for form 8839 might be helpful.
http://www.irs.gov/pub/irs-pdf/i8839.pdf