Hi
As you will see below putting in a new SIM card won't make any difference. You need a tri band phone in order to make such calls from the US (if you don't have one of these it will not work regardless). Also you must bear in mind that such calls will cost you a lot even if you're talking for only a short time.
The first thing you will need to do if you have never used your Mobile Phone or your Sim card abroad before is to contact your Service or Network provider and ask them to remove the International Call Bar. You should be able to find the phone number to contact them on your Phone bill.
At the same time it will be worth letting them know where you are planning to travel to as they will advise you if there are any problems with using your phone there.
All numbers you call from your mobile must be prefixed with the international code of the country you are calling. Your service provider will be able to advise you of exactly how to do this.
You must always ensure that your Mobile Phone is switched off before entering an aircraft and is not switched back on until you have alighted the Plane and are back in the Airport Terminal. This is due to the risk of the signal from your phone affecting the instrumentation of the Plane. It is therefore in your best interest to abide by this rule.
The first thing to note is that you WILL be charged for calls you receive when you are abroad. This is because you pick up the international "leg" of any calls. This may seen unreasonable, but callers may not know you are overseas or not be prepared to pay an international call charge. If you want to avoid being charged in this way, you can set your phone to divert to voicemail and retrieve messages later. The coverage, services and charges offered are those of the foreign network.
The USA uses a slightly different GSM frequency for standard Mobile Phone calls than most other countries so you will need to have a tri-band phone such as the Sony Ericsson P900 or the Nokia 7250. Tri band phones are quite common nowadays to check the manual that came with your phone to see if it has this feature. When using a Tri-band phone in America, it will automatically switch to the correct frequency to allow you to recieve signals.
A cheaper way of contact is to buy a pre-paid telephone card (you call a number and that accesses the exchange) that you can use from any telephone.