Hi,
I finally got the apostilled FBI letter a few months ago. Here are the steps required:
1) Submit the request for the FBI criminal background check. In the cover letter request a certified version (has the FBI seal and signature). If I did it again I'd underline and bold the request for a certified version, because they forgot to do it for me, which required several calls and faxes to resolve it.
2) Once you receive that back (took 6-8 weeks for me), you send it to the US State Department (go to their website for address and info) to request the FBI letter to be apostilled. That is quite quick (about a week including mail), and if you happen to be in the DC area, you can get it done at the office. They attach a little piece of paper that says it is appostiled.
3)That's it! I believe Argentina accepts it for only 3 months, but I'm not certain about that.
On a side note, if you are getting your birth certificate appostiled, the state government where you were born does that one.