If you intend to undertake a formal course of training in the USA, you will need a
visa. If you intend only to hour-build, your flying is essentially recreational and is covered by the Visa Waiver scheme. You may, however, have to have written confirmation of your initial aircraft hire arrangements on entry to the USA. Check with the US Embassy's website for further information.
The Private Flying forum may well have more information regarding licencing requirements for recreational flying in the USA.
Scroggs