Although there is some variation depending on the country from which you are calling, it is necessary to dial a certain set of digits prior to dialing the recipient's mobile phone number. In European countries, you need to dial "001" before calling the United States.
It is still necessary to know the area code of the individual you are trying to reach, as that area code must be dialed after you dial "001." It is easier to think of the "001" as an international area code that you need to dial prior to dialing the local area code. Since "00" is the European international access code, the numbers are likely to differ when calling from non-European countries.