We received Noah's SSN the other day. This marks the end of all the post-adoption paperwork we had to get (besides on-going post placement reports.) The visit to the SSN office was fairly straight forward.

Only one parent needs to go and your child does NOT need to go either.  This makes the trip easier.  We took Noah's passport, readoption paperwork that we received here in the US and all his paperwork from Ethiopia (Ethiopian passport, court decree, birth certificate, etc.) just to be safe.  You will also need the driver's license or passport of the parent visiting the office.  Once I got there I signed-in and filled out the application while I waited.  After about 40 minutes they called me up and it only took about 15 minutes to go through all the paperwork with the agent. 

It didn't cost anything and we ended up receiving Noah's SSN card in about 10 days!