If you're just flying with an instructor, nothing special is required - turn up at a local flying school and go flying.
If you're training for a license or a rating, though (which I assume you're not from your post) then you will need a Visa. I won't go into details, because I don't think it applies to you - but I mention it because although you now know the rules, there is no guarantee that the person working the immigration desk knows the rules, and when you arrive in the country, if he finds out that you'll be flying, but doesn't understand the difference between formal training and what you're proposing to do, then you will be coming home on the next plane.
If you're planning on flying solo, then you will need an FAA license. You need to contact the FAA and get an application form, fill it in, and send it back to them. You then need to download the appropriate form from the CAA website, and send that in to the CAA along with a cheque. The CAA, on receiving your money, will confirm to the FAA that your license is real. When they receive this confirmation, the FAA will write to you to let you know that you can pick your license up from the FSDO (which you will have to nominate in advance - ask your chosen flying school in the US where the nearest one is). Allow a couple of months for this process.
Hope that helps,
FFF
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<<edit: or a medical and student pilot certificate, FFF>>
Last edited by Keygrip; 7th Jan 2004 at 19:47.