You are talking about the child and dependent care credit. You can claim a credit (not a deduction) on up to $3000 of care costs for one child or $6000 of care costs for 2 or more children, if you pay for care so that you (and your spouse if married) can work or go to school full time. The credit is between 20% and 35% of the eligible cost of care, depending on your income.
When you hire a nanny, you are responsible for household employees tax. That's about 15% of their gross wages. Here is the correct way to do this. Suppose the wage is $100. You would deduct $6.20 for social security and $1.45 for Medicare, and actually pay the nanny $92.35. At the end of the year, you would give the nanny a W-2 showing $100 of wages and $6.20 and $1.45 of medicare withholding. On your tax return, you would pay household employee tax of $15.30 (half is the amount you withheld and half is your match) based on the $100 of gross wages.
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Now going back to the child and dependent care credit, the amount of "expense" you can claim for the credit is the gross wages you paid plus your share of the household employee tax, or $107.65.
