As stated you have two options depending on what you wish to do flying wise in the USA.
If you wish to rent an a/c for pleasure flying or hour building you need to do this:
You must get an FAA PPL based on your foreign licence.
You must contact a FSDO (Flight Standards Ditrict Office) they are all over the states and depending on where you will be initially in the USA will most probably be the deciding factor on which FAA FSDO you choose to contact.
From here on it's a paper exercise. You can get the paperwork rolling before you are in the USA and this is probably a good idea. But you must go into the FSDO in person to be issued with your "temperoary AirMan Cert" This cert is good to fly on as it takes 4-6 months for your little green FAA PPL to be issued in the mail/post!
Your FAA PPL that you now have is issued on the basis of your foreign licence. All limitations and restrictions on your foreign licence apply on your FAA PPL. Your FAA PPL is only valid for as long as your foreign licence is current and your foreign medical is current. If your foreign medical is current, you do not need an FAA medical.
Nearly there... Now you have all your paperwork except your BFR (Bienneal Flight Review) No problem. Wherever you are renting the a/c from, they will undoubtely have at least an hour check out for insurance purposes, so you can most likely combine your check out and BFR in the same flight.
A BFR must be taken once every 2 years as part of the FAA currency regulations. It consists of at least 1 hour flying with an instuctor and 1 hour ground work with an instuctor. It is not an exam. But essential for you, to ensure you are familiar with the US airspace, R/T, and regulations, as they are quite different from JAR land!!
Get your BFR logged and signed in your logbook by the CFI who done the BFR and you are now free to fly stateside.
If you wish to gain FAA ratings such as FAA ME/IR/CFI/CPL etc..
You require an M1 visa. TSA(Transport Security Administation) clerance and fingerprinting. Sounds like a lot, but it is relitavely simple. You will need to contact a school in the states about this because you require the school to register you as a student with SEVIS, stating you will be training at their school. Again a lot of paperwork but contact the school and it will all make sense.
Thats it!!
Enjoy America.