How do I claim the adoption credit?
You can calculate and claim your adoption credit by using Form 8839, which should then be attached to either Form 1040 or Form 1040A. You cannot claim the adoption credit if you are using Form 1040EZ, and if you are married, you must be filing jointly to claim the adoption credit.
As for when you can claim the adoption credit, you must look at both the nationality of the adopted child and when the adoption expenses were paid. If the child is a foreign child, you cannot take the adoption credit until the adoption becomes final - so any expenses from earlier years cannot be applied toward the adoption credit until the year in which the adoption is finalized. Any expenses from the adoption after it has been finalized can be put towards the adoption credit for the year in which the expenses were paid.
If the adopted child is a citizen or resident of the United States, you do not have to wait for the adoption to be finalized before claiming adoption related expenses. Expenses paid in any years before the adoption was finalized can be claimed in the following year, any expenses paid in the year the adoption becomes final can be claimed in that year and any expenses paid in the years after the adoption was finalized can be claimed in the year they are paid.