Check out Form 2555
You use this form: If you are a U.S. citizen or a resident alien.
• Earned wages/salaries in a foreign country.
• Had total foreign earned income of $95,100 or less.
• Are filing a calendar year return that covers a 12-month period.
And You:
• Do not have self-employment income.
• Do not have business/moving expenses.
• Do not claim the foreign housing exclusion or deduction.
Also the UK and the US have a tax treaty you will want to look into also
If you have any more questions just ask!
Each state has its own rules about whom it considers a resident and who is required to file a state tax return.