My family will be migrated to USA shortly. I'd like to find out how much non-taxable money can I bring in to USA? Also would like to know the process and procedure of declaring such money for non-taxable income. My landed province is California.

QUOTE," how much non-taxable money can I bring in to USA? "---Anyone can bring unlimited amounts of money into the United States from overseas. But if the amount of money coming into the US from abroad via wire transfer( into your bank account) exceeds $10,000 , then your bank will report the amount to the Fed. Or IRS( US Treaury Dpt).That doesn't mean to pay any form of taxes on the money transferred into the US from overseas.Federal law requires that all banks report any cash deposits made in excess of $10,000 in the hopes of discouraging money laundering, rather than tax evasion. "wires" from abroad require the same information.
However, you may choose to bring large sums of money with you in the form of cash, money order, or traveler's checks or etc. when entering the U.S. any amounts of money exceeding the allowed $10,000 maximum MUST BE DECLARED in advance.
When you arrive in the U.S. you are required to declare all monies that you are bringing into the country. You will receive Form 6059B Customs Declaration, which must be filled in completely and truthfully. If you do not declare your money, the penalties for non-compliance can be SEVERE. Your money might be TAKENAWAY. So,you will be required to provide a written explanation of your failure to comply, your case will be evaluated, and you might have to pay a considerable fine.