How does extra withholding from each paycheck work when filing taxes? Is it lumped into the federal tax return or the state? Do I have to itemize and somehow claim that I had extra withholding? How do I find out that I'm actually getting the money back that I had withheld?
The extra amount is lumped in with the rest of your withholding. All you do is enter your W-2 as you normally do. There is no guarantee that you will get the entire amount back. That depends on how much taxable income you have.
The W-2 you get at the end of the year should include the total of all that was withheld, all added together.
"Total" of all Federal withholding is in box 2
"Total" of all State withholding is in box 17
As leeloo posted, your total withholding, whether part of the regular calculation or the extra you noted on your W4, is reported in box 2 for federal and box 17 for state of your Form W-2 you receive from your employer.
Once you have entered your W-2 into TurboTax, the software will walk you through a series of other questions based on the forms you received and input to determine your taxable income and therefore your refund or tax amount due.