It used to be simple!!!!!
Long gone are the days of popping down the FBO and getting a temp Airmans Cert issued on the basis of your CAA/JAA.
You now need to fill out a form located on the FAA website, send that with photo copies of licence, medical etc to the FAA office in Oklahoma, then fill out a form from the CAA (also on website) pay them £15 to veryfy your licence to the FAA. Choose what FBO you want your licence issued at and then wait............ they say up to 3 months. I got my authorisation after about 6 weeks.
Hope this helps.