If the phone supports the US GSM bandwidth then it will work with the GSM carriers there (AT&T & T-Mobile) But you must also make sure that the phone is NOT locked to any carrier, in which case you will need to get the phone unlocked and then you will be able to use it with any GSM simcard - To unlock the phone call the original carrier or take it to a phone tech store to get unlocked or buy an unlocked code online.
HI is your Nokia 3110c mobile is not working in USA with their local GSM sim then it mean your phone might be locked with some other network provider in other countries ...You can easily fix it by unlocking your phone from its present network provider .You can easily unlock your phone using sites like TheUnlockArena.com they are rendering network unlock code for all mobile models at reliable cost .You first check that whether the code is available for your country and network provider .If yes then pay for it and unlock your phone then freely use it with any GSM sim ...