For all foreign nationals in the US who are 14 or older, properly notifying the US government of an address change in a timely manner is critical. Why is it so important? US Immigration Judges order countless thousands of people "removed" (deported) from the US every year simply because the foreign national has failed to appear to US Immigration Court. (Such an order of deportation is called an "in absentia" order. If you ever get one of these, hire an experienced deportation lawyer immediately.) Removal proceedings are unlike criminal proceedings in a great many ways, and this is one example. People are rarely convicted of a crime 'in absentia" but they are ordered deported in absentia every workday.
The preferred method for changing a foreign national's address is for each foreign national to call the National Customer Service Center toll free at 1-800-375-5283.
The available form that foreign nationals may be able to use to change their address (when they are not in removal proceedings) is form AR-11, available at www.uscis.gov. To find this or any of the plethora of free forms available from USCIS ("US Citizenship and Immigration Services"), go to www.uscis.gov and click on the word "forms" or "FORMS," and scroll down to whatever form you need. The Form AR-11 is an easy form to fill out. Technically, a foreign national's address change needs to be filed within ten days of moving. Even if you blow this deadline, at least change your address with USCIS before the US government sends you any mail. Certain pieces of mail, containing green cards, for example, will not be forwarded by the US Postal Service, but will be returned to the Service Center that sent it. Having your mail forwarded by the US Postal Service is easy enough to do, it just won't work for forwarding security documents like green cards or work permits. Just go to your local Post Office and fill out the form. But forwarding your mail is NOT a substitute for changing your address with the USCIS, Department of Homeland Security, (or with the US Immigration Court, which has it's own form EOIR 33 for changing addresses, or for sponsors filing form I-864.)
Disclaimer: This comes as general information, and is not intended for specific applications. I suggest discussing your personal details with an experienced immigration attorney.