Just like in the United States, your device must be unlocked by your carrier or manufacturer before switching.
Most international phones run off GSM technology. However, some devices are also known to have dual SIM's meaning they can read both GSM and CDMA technology.
GSM carriers in the United States are T-Mobile and AT&T.
CDMA carriers in the United States are Sprint, Verizon and US Cellular.
If your device is unlocked and compatible with the carriers in the United States then it will be no problem plugging in a U.S. SIM card once you move. Make sure to purchase a SIM card that fits your device and a plan that best suits your cellular needs.
Be aware that not all services may be available, your phone may operate ona slightly different frequency of GSM than the US carriers, you may only be able to get 3G data speeds rather than 4G LTE - fine in the short term, however if you are planning to be in the US for longer then you may want to consider buying a new phone to access all services at full speed
Click here to Compare GSM BYO Options
And if you have a dual SIM,
Click here to Compare Sprint CDMA BYO Options
Click here to Compare Verizon CDMA BYO Options