This article is from the Aviation FAQ, by Geoffrey G. Peck firstname.lastname@example.org with numerous contributions by others.
In general, a pilot's license entitles you to fly aircraft of the same
country of registry as your license _anywhere_ in the world. So if
you can find an airplane registered in your "home" country, there's
no problem. For most non-U.S. pilots, if you wish to obtain a U.S.
pilot's certificate, simply present your existing pilot certificate at
any FAA FSDO (acronyms below), and you will receive free of charge an
equivalent U.S. certificate (private and instrument ratings only).
Note that non-governmentally regulated licenses, such as a BGA or
FAI badge issued by the British Gliding Association, will _not_ be
honored by the FAA. (In this particular case, experienced British
glider pilots will usually have no trouble having a U.S. flight
instructor issue a U.S. student pilot certificate as part of the
checkout process. This will be valid for restricted solo flight.)
Some FSDOs also require a current medical certificate; you will
probably be able to use your "home" medical. But call the FSDO
before you visit. You can then legally fly U.S.-registered