If you want to use your mobile in the USA it needs to be either a tri-band or a quad-band. If you use your UK mobile sim card in the USA it will be very expensive to make and to receive calls. It is often free to receive texts.
If you want to make calls within the USA or access the internet (either on a smartphone or tethered to a laptop or tablet) I suggest you buy a sim USA card. However, not all providers use the GSM system as we do. T-Mobile uses our system and they are the one I used during a recent visit. You can choose pre-paid pay as you go or you can opt for $1 or $2 per day (only on days it is used). For $2 per day you can get unlimited calls within the US and unlimited internet (2G). My sim card cost me $10. You can see these rates on
http://prepaid-phones.t-mobile.com/pay-as-you-go-plans
http://prepaid-phones.t-mobile.com/pay-by-the-day-cell-phone-plans
If you want to make calls to the UK I suggest you buy a “calling card”. I paid $5 for a calling card and got calls to the UK for a few cents per minute. These can be used from mobiles or land lines. The cost per minute varies depending on if you use a local access number or a Freephone number. You can buy these over the internet or in shops in the US. If you buy over the internet they email the pin number so you can use them straight away.
I used my US sim on the $2 per day tariff and used this to phone a local access number. In this way I got the cheapest rate.