Congratulations on your decision to adopt. As an adoptive mom myself, I can relate to all of the questions you must have, including those around cost.
Adoption expenses vary greatly depending on the type of adoption you choose, e.g., domestic vs. international, public vs. private, and agency vs. independent. Typical expenses vary from less than $10,000 up to $40,000 or more. Special needs adoption fees are usually lower and may be fully subsidized.
A good summary of adoption costs is provided by the U.S. Department of Health and Human Services in a fact sheet found here. This fact sheet also describes various resources available to offset these costs, such as tax credits, special loans and grants, and benefits available from some employers.
As you start to work with an agency, review specific costs with them and ask for references. As you interview adoptive parents, make sure you ask them if there were any surprises in working with the agency, including expenses that they had not been aware of.
I wish you the best as you move forward with your adoption.