I just sent my fingerprints and form in to the FBI with a Fedex account number to send to my U.S. address. I previously did this for my Argentine DNI but now I'm in the U.S. again and I need it for employment here.
The current wait times are about 8 weeks. After 4 weeks you can begin calling to see what the status is - google them for the specific phone number. My credit card was charged about 4 weeks after I sent the document, so I know they are processing it. When I called they said it was still in process and that I should call back.
Regarding the apostille, the FBI used to not condone this, but as of 2010 you may in fact take the certificate to the State Department to be apostill'd. Unfortunately this is one extra annoying step. You can do this along with your birth cert or whichever materials you needed apostill'd. The safest option is to have the FBI send your clearance to a family member in the U.S. who can then take your stuff to be apostill'd. Check the State Dept website to see if there is a place locally (in the U.S.) that will do apostilles. Otherwise I think you have to send it to the State Dept office usually in the Capital of the state.
http://www.state.gov/m/a/auth/
From the FAQ on the FBI website at:
http://www.fbi.gov/about-us/cjis/background-checks/faqs
9. Does the FBI provide apostilles*?
(*An apostille is a certification that a document has been “legalized” or “authenticated” by the issuing agency through a process in which various seals are placed on the document.)
The CJIS Division will authenticate U.S. Department of Justice Order 556-73 fingerprint search results for international requests by placing the FBI seal and the signature of a division official on the results if requested at the time of submission. Documents prepared in this way may then be sent to the U.S. Department of State by the requestor to obtain an apostille if necessary. This procedure became effective on January 25, 2010 and will apply only to documents finalized after that date. Requests to authenticate previously processed results will not be accepted. This procedure replaces the letter formerly provided by the CJIS Division that indicated the service was not provided. Note: FBI-approved Channelers cannot provide an apostille. A request for your FBI Identification Record must be submitted directly to the FBI if an apostille is needed.
Hope that helps! Sorry I don't have more info because I'm not doing it for Argentina this time!