To fly as PIC in the States you'll need to get an FAA certificate. You will want to start this proces as soon as possible as it takes about 8 weeks to get the verification letter from the FAA.
You begin the process by faxing the submission form (available on the FAA website), along with copies of your license, medical and some ID to the FAA office in Oklahome City. On this form you specify which local FAA office you want to visit for issue of the cerificate. Once your apllication is processed, they will send you a verification letter stating you can now go to the FAA office you have chosen.
**Important** After you get the letter call your chosen FAA office and verify they have received their authorization from Oklahoma City. Once you have confirmed this you need to make an appointment to visit that office. When you show up, bring ID, your license and medical. You will also be going through airport style security to get into the building.
After that it is just filling out some documents and they will issue your certificate.