Katharine:
Your position will be considered a trainee position as defined by IRS Pub 519 (which can be downloaded as a PDF document from
www.irs.gov).
This makes you an "exempt individual" for the Substantial Presence Test provisions. If you are taxed at all (contact your employer's Human Resources department to check this out; you
may be completely exempt from taxation), you will be taxed as a non-resident alien. This means you file Form 1040NR.
If you are exempt from all taxation (I am pretty sure you are exempt from the Social Security and Medicare taxes, but not so sure about the federal income taxes), you
still have to file Form 8843 annually. Procedues for filing this form can be found in the IRS Pub 519 cited above. The on-line pub is for 2004, but provisions have not change in the past year so they apply equally to 2005 and, for now, 2006.