Contact the financial institution that issued your debit card immediately by phone or in writing. Under the Electronic Funds Transfer Act, the institution has 60 days to investigate fraudulent charges after the date the first statement containing them is mailed to you.
The Federal Reserve Board notes that if you report the fraud within two business days, liability is limited to $50. If you report it after that, you could face liability of up to $500, and if you report it after the 60-day window, subsequent fraudulent charges can wipe out your account entirely.
Have the relevant information available for your financial institution if speaking by phone or writing a letter. The FRB advises giving your name, account number, date and amount of the debit card fraud(s), and the reason you believe the charges to be fraudulent.
Expect to have your case resolved within 45 days, or 90 days, if your account is new (less than 30 days old) or if the fraudulent charges were point-of-service or foreign transactions. Your bank may replace the money wrongly taken from you pending investigation and outcome.