The place to start is:
http://www.irs.gov/pub/irs-pdf/p968.pdf
If you call the IRS, you will get a different answer from each person you reach. For 2004, the credit was raised to $10,390. If your adoption attempt was domestic, you should be able to take a seperate credit for each attempt. You only get the actual expenses for the attempt. The new rules for 2004 are in this publication.
I hope that you will be able to take a credit for a successful adoption next year!
Peggy