I took an Australian ATPL with CIR over to the US in 1995 and went for a US ATPL. I already had a commercial US license on seaplanes. So heres what happened.
I had to get my logbook checked by the FAA before they allowed me to sit the ATPL exam, which was done at a FBO on a computer and the result sent back within an hour. To prepare for the exam I had obtained and studied all the relevant FAR's as well as the Gleims Red Books on both Instrument and ATPL subjects. Good books for preparation these. I also had to do a flight in a light twin with an examiner of airmen, with a oral quiz before take off and the flight was much as it is in Australia. Note I already had an Aussie ATPL, so theres no rubber stamp method of getting it done. I took a light single around the area for days beforehand shooting approaches to get the gist of the place.
Also note I did it with a small FBO.. most guys do all this with the sausage factories like Flight Safety. Another think.. an aquaintance of mine was knocked back because the FAA didnt accept the copy of his log after the original had been destroyed/ lost, so cross the t's and dot the i's. I chose to get a Commercial first by doing floatplane training and the experience was invaluable ( and fun ).
Hope this helps. From memory they will let you fly in the US privately after a check out but I never tried this.